diff --git a/CHANGES.rst b/CHANGES.rst
index bf8ce262..70f85e95 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -27,6 +27,23 @@
 
   See `issue 200 <https://github.com/zopefoundation/zope.interface/issues/200>`_.
 
+- Require that the second argument (*bases*) to ``InterfaceClass`` is
+  a tuple. This only matters when directly using ``InterfaceClass`` to
+  create new interfaces dynamically. Previously, an individual
+  interface was allowed, but did not work correctly. Now it is
+  consistent with ``type`` and requires a tuple.
+
+- Let interfaces define custom ``__adapt__`` methods. This implements
+  the other side of the :pep:`246` adaptation protocol: objects being
+  adapted could already implement ``__conform__`` if they know about
+  the interface, and now interfaces can implement ``__adapt__`` if
+  they know about particular objects. There is no performance penalty
+  for interfaces that do not supply custom ``__adapt__`` methods.
+
+  This includes the ability to add new methods, or override existing
+  interface methods using the new ``@interfacemethod`` decorator.
+
+  See `issue 3 <https://github.com/zopefoundation/zope.interface/issues/3>`_.
 
 5.0.2 (2020-03-30)
 ==================
diff --git a/docs/README.rst b/docs/README.rst
index 6fbd5f83..0364a816 100644
--- a/docs/README.rst
+++ b/docs/README.rst
@@ -863,7 +863,8 @@ Adaptation
 
 Interfaces can be called to perform adaptation.
 
-The semantics are based on those of the PEP 246 ``adapt`` function.
+The semantics are based on those of the  :pep:`246` ``adapt``
+function.
 
 If an object cannot be adapted, then a ``TypeError`` is raised:
 
@@ -897,7 +898,13 @@ If an object already implements the interface, then it will be returned:
   >>> I(obj) is obj
   True
 
-If an object implements ``__conform__``, then it will be used:
+:pep:`246` outlines a requirement:
+
+    When the object knows about the [interface], and either considers
+    itself compliant, or knows how to wrap itself suitably.
+
+This is handled with ``__conform__``. If an object implements
+``__conform__``, then it will be used:
 
 .. doctest::
 
@@ -936,21 +943,27 @@ Adapter hooks (see ``__adapt__``) will also be used, if present:
   >>> class I(zope.interface.Interface):
   ...     pass
 
-Interfaces implement the PEP 246 ``__adapt__`` method.
+Interfaces implement the :pep:`246` ``__adapt__`` method to satisfy
+the requirement:
+
+    When the [interface] knows about the object, and either the object
+    already complies or the [interface] knows how to suitably wrap the
+    object.
 
-This method is normally not called directly. It is called by the PEP
-246 adapt framework and by the interface ``__call__`` operator.
+This method is normally not called directly. It is called by the
+:pep:`246` adapt framework and by the interface ``__call__`` operator.
 
 The ``adapt`` method is responsible for adapting an object to the
 reciever.
 
-The default version returns ``None``:
+The default version returns ``None`` (because by default no interface
+"knows how to suitably wrap the object"):
 
 .. doctest::
 
   >>> I.__adapt__(0)
 
-unless the object given provides the interface:
+unless the object given provides the interface ("the object already complies"):
 
 .. doctest::
 
@@ -989,6 +1002,28 @@ Hooks can be uninstalled by removing them from the list:
   >>> I.__adapt__(0)
 
 
+It is possible to replace or customize the ``__adapt___``
+functionality for particular interfaces.
+
+.. doctest::
+
+   >>> class ICustomAdapt(zope.interface.Interface):
+   ...     @zope.interface.interfacemethod
+   ...     def __adapt__(self, obj):
+   ...          if isinstance(obj, str):
+   ...              return obj
+   ...          return super(type(ICustomAdapt), self).__adapt__(obj)
+
+   >>> @zope.interface.implementer(ICustomAdapt)
+   ... class CustomAdapt(object):
+   ...    pass
+   >>> ICustomAdapt('a string')
+   'a string'
+   >>> ICustomAdapt(CustomAdapt())
+   <CustomAdapt object at ...>
+
+.. seealso:: :func:`zope.interface.interfacemethod`
+
 .. [#create] The main reason we subclass ``Interface`` is to cause the
              Python class statement to create an interface, rather
              than a class.
diff --git a/docs/api/declarations.rst b/docs/api/declarations.rst
index 955d2462..fa265e7a 100644
--- a/docs/api/declarations.rst
+++ b/docs/api/declarations.rst
@@ -36,6 +36,8 @@ To declare an interface itself, extend the ``Interface`` base class.
 
    .. documented in README.rst
 
+.. autofunction:: interfacemethod
+
 Declaring The Interfaces of Objects
 ===================================
 
diff --git a/src/zope/interface/__init__.py b/src/zope/interface/__init__.py
index e282fbda..3372103e 100644
--- a/src/zope/interface/__init__.py
+++ b/src/zope/interface/__init__.py
@@ -49,7 +49,7 @@ def meth(arg1, arg2):
 See the module doc strings for more information.
 """
 __docformat__ = 'restructuredtext'
-
+# pylint:disable=wrong-import-position,unused-import
 from zope.interface.interface import Interface
 from zope.interface.interface import _wire
 
@@ -75,8 +75,11 @@ def meth(arg1, arg2):
 from zope.interface.declarations import noLongerProvides
 from zope.interface.declarations import providedBy
 from zope.interface.declarations import provider
+
 from zope.interface.exceptions import Invalid
+
 from zope.interface.interface import Attribute
+from zope.interface.interface import interfacemethod
 from zope.interface.interface import invariant
 from zope.interface.interface import taggedValue
 
diff --git a/src/zope/interface/_zope_interface_coptimizations.c b/src/zope/interface/_zope_interface_coptimizations.c
index 69f5bbcf..346e7f2d 100644
--- a/src/zope/interface/_zope_interface_coptimizations.c
+++ b/src/zope/interface/_zope_interface_coptimizations.c
@@ -49,6 +49,8 @@ static PyObject *str_registry, *strro, *str_generation, *strchanged;
 static PyObject *str__self__;
 static PyObject *str__module__;
 static PyObject *str__name__;
+static PyObject *str__adapt__;
+static PyObject *str_CALL_CUSTOM_ADAPT;
 
 static PyTypeObject *Implements;
 
@@ -796,7 +798,7 @@ static struct PyMethodDef ib_methods[] = {
 
 */
 static PyObject *
-ib_call(PyObject *self, PyObject *args, PyObject *kwargs)
+IB_call(PyObject *self, PyObject *args, PyObject *kwargs)
 {
   PyObject *conform, *obj, *alternate, *adapter;
   static char *kwlist[] = {"obj", "alternate", NULL};
@@ -835,7 +837,23 @@ ib_call(PyObject *self, PyObject *args, PyObject *kwargs)
       Py_DECREF(conform);
   }
 
-  adapter = __adapt__(self, obj); // XXX: should be self.__adapt__.
+  /* We differ from the Python code here. For speed, instead of always calling
+     self.__adapt__(), we check to see if the type has defined it. Checking in
+     the dict for __adapt__ isn't sufficient because there's no cheap way to
+     tell if it's the __adapt__ that InterfaceBase itself defines (our type
+     will *never* be InterfaceBase, we're always subclassed by
+     InterfaceClass). Instead, we cooperate with InterfaceClass in Python to
+     set a flag in a new subclass when this is necessary. */
+  if (PyDict_GetItem(self->ob_type->tp_dict, str_CALL_CUSTOM_ADAPT))
+  {
+      /* Doesn't matter what the value is. Simply being present is enough. */
+      adapter = PyObject_CallMethodObjArgs(self, str__adapt__, obj, NULL);
+  }
+  else
+  {
+      adapter = __adapt__(self, obj);
+  }
+
   if (adapter == NULL || adapter != Py_None)
   {
       return adapter;
@@ -1045,7 +1063,7 @@ static PyTypeObject InterfaceBaseType = {
         /* tp_as_sequence    */ 0,
         /* tp_as_mapping     */ 0,
         /* tp_hash           */ (hashfunc)IB_hash,
-        /* tp_call           */ (ternaryfunc)ib_call,
+        /* tp_call           */ (ternaryfunc)IB_call,
         /* tp_str            */ (reprfunc)0,
         /* tp_getattro       */ (getattrofunc)0,
         /* tp_setattro       */ (setattrofunc)0,
@@ -2023,6 +2041,8 @@ init(void)
   DEFINE_STRING(__self__);
   DEFINE_STRING(__name__);
   DEFINE_STRING(__module__);
+  DEFINE_STRING(__adapt__);
+  DEFINE_STRING(_CALL_CUSTOM_ADAPT);
 #undef DEFINE_STRING
   adapter_hooks = PyList_New(0);
   if (adapter_hooks == NULL)
diff --git a/src/zope/interface/common/__init__.py b/src/zope/interface/common/__init__.py
index a8bedf06..b40c3178 100644
--- a/src/zope/interface/common/__init__.py
+++ b/src/zope/interface/common/__init__.py
@@ -259,5 +259,5 @@ def getRegisteredConformers(self):
         return set(itertools.chain(registered, self.__extra_classes))
 
 
-ABCInterface = ABCInterfaceClass.__new__(ABCInterfaceClass, None, None, None)
+ABCInterface = ABCInterfaceClass.__new__(ABCInterfaceClass, 'ABCInterfaceClass', (), {})
 InterfaceClass.__init__(ABCInterface, 'ABCInterface', (Interface,), {})
diff --git a/src/zope/interface/interface.py b/src/zope/interface/interface.py
index d035ade0..ff26d333 100644
--- a/src/zope/interface/interface.py
+++ b/src/zope/interface/interface.py
@@ -20,6 +20,7 @@
 import weakref
 
 from zope.interface._compat import _use_c_impl
+from zope.interface._compat import PYTHON2 as PY2
 from zope.interface.exceptions import Invalid
 from zope.interface.ro import ro as calculate_ro
 from zope.interface import ro
@@ -36,7 +37,10 @@
 
 CO_VARARGS = 4
 CO_VARKEYWORDS = 8
+# Put in the attrs dict of an interface by ``taggedValue`` and ``invariants``
 TAGGED_DATA = '__interface_tagged_values__'
+# Put in the attrs dict of an interface by ``interfacemethod``
+INTERFACE_METHODS = '__interface_methods__'
 
 _decorator_non_return = object()
 _marker = object()
@@ -651,6 +655,21 @@ def __repr__(cls):
 )
 
 
+def interfacemethod(func):
+    """
+    Convert a method specification to an actual method of the interface.
+
+    This is a decorator that functions like `staticmethod` et al.
+
+    The primary use of this decorator is to allow interface definitions to
+    define the ``__adapt__`` method.
+    """
+    f_locals = sys._getframe(1).f_locals
+    methods = f_locals.setdefault(INTERFACE_METHODS, {})
+    methods[func.__name__] = func
+    return _decorator_non_return
+
+
 class InterfaceClass(_InterfaceClassBase):
     """
     Prototype (scarecrow) Interfaces Implementation.
@@ -664,6 +683,57 @@ class InterfaceClass(_InterfaceClassBase):
     #
     #implements(IInterface)
 
+    def __new__(cls, name=None, bases=(), attrs=None, __doc__=None, # pylint:disable=redefined-builtin
+                __module__=None):
+        assert isinstance(bases, tuple)
+        attrs = attrs or {}
+        needs_custom_class = attrs.pop(INTERFACE_METHODS, None)
+        if needs_custom_class:
+            needs_custom_class.update(
+                {'__classcell__': attrs.pop('__classcell__')}
+                if '__classcell__' in attrs
+                else {}
+            )
+            if '__adapt__' in needs_custom_class:
+                # We need to tell the C code to call this.
+                needs_custom_class['_CALL_CUSTOM_ADAPT'] = 1
+
+            if issubclass(cls, _InterfaceClassWithCustomMethods):
+                cls_bases = (cls,)
+            elif cls is InterfaceClass:
+                cls_bases = (_InterfaceClassWithCustomMethods,)
+            else:
+                cls_bases = (cls, _InterfaceClassWithCustomMethods)
+
+            cls = type(cls)( # pylint:disable=self-cls-assignment
+                name + "<WithCustomMethods>",
+                cls_bases,
+                needs_custom_class
+            )
+        elif PY2 and bases and len(bases) > 1:
+            bases_with_custom_methods = tuple(
+                type(b)
+                for b in bases
+                if issubclass(type(b), _InterfaceClassWithCustomMethods)
+            )
+
+            # If we have a subclass of InterfaceClass in *bases*,
+            # Python 3 is smart enough to pass that as *cls*, but Python
+            # 2 just passes whatever the first base in *bases* is. This means that if
+            # we have multiple inheritance, and one of our bases has already defined
+            # a custom method like ``__adapt__``, we do the right thing automatically
+            # and extend it on Python 3, but not necessarily on Python 2. To fix this, we need
+            # to run the MRO algorithm and get the most derived base manually.
+            # Note that this only works for consistent resolution orders
+            if bases_with_custom_methods:
+                cls = type( # pylint:disable=self-cls-assignment
+                    name + "<WithCustomMethods>",
+                    bases_with_custom_methods,
+                    {}
+                ).__mro__[1] # Not the class we created, the most derived.
+
+        return _InterfaceClassBase.__new__(cls)
+
     def __init__(self, name, bases=(), attrs=None, __doc__=None,  # pylint:disable=redefined-builtin
                  __module__=None):
         # We don't call our metaclass parent directly
@@ -738,7 +808,7 @@ def update_value(aname, aval):
                 # __qualname__: PEP 3155 (Python 3.3+)
                 '__qualname__',
                 # __annotations__: PEP 3107 (Python 3.0+)
-                '__annotations__'
+                '__annotations__',
             )
             and aval is not _decorator_non_return
         }
@@ -889,6 +959,11 @@ def __reduce__(self):
 Specification._ROOT = Interface
 ro._ROOT = Interface
 
+class _InterfaceClassWithCustomMethods(InterfaceClass):
+    """
+    Marker class for interfaces with custom methods that override InterfaceClass methods.
+    """
+
 
 class Attribute(Element):
     """Attribute descriptions
diff --git a/src/zope/interface/interfaces.py b/src/zope/interface/interfaces.py
index c0ece6ae..6321d0c4 100644
--- a/src/zope/interface/interfaces.py
+++ b/src/zope/interface/interfaces.py
@@ -518,6 +518,35 @@ class IRange(Interface):
         .. seealso:: `zope.interface.invariant`
         """
 
+    def interfacemethod(method):
+        """
+        A decorator that transforms a method specification into an
+        implementation method.
+
+        This is used to override methods of ``Interface`` or provide new methods.
+        Definitions using this decorator will not appear in :meth:`IInterface.names()`.
+        It is possible to have an implementation method and a method specification
+        of the same name.
+
+        For example::
+
+           class IRange(Interface):
+                @interfacemethod
+                def __adapt__(self, obj):
+                    if isinstance(obj, range):
+                       # Return the builtin ``range`` as-is
+                       return obj
+                    return super(type(IRange), self).__adapt__(obj)
+
+        You can use ``super`` to call the parent class functionality. Note that
+        the zero-argument version (``super().__adapt__``) works on Python 3.6 and above, but
+        prior to that the two-argument version must be used, and the class must be explicitly
+        passed as the first argument.
+
+        .. versionadded:: 5.1.0
+        .. seealso:: `zope.interface.interfacemethod`
+        """
+
     ###
     # Querying interfaces
     ###
diff --git a/src/zope/interface/tests/test_adapter.py b/src/zope/interface/tests/test_adapter.py
index 869df663..8ff96f06 100644
--- a/src/zope/interface/tests/test_adapter.py
+++ b/src/zope/interface/tests/test_adapter.py
@@ -796,12 +796,12 @@ def test_ctor_w_registry_provided(self):
         from zope.interface import Interface
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         alb = self._makeOne(registry)
         self.assertEqual(sorted(alb._extendors.keys()),
                          sorted([IBar, IFoo, Interface]))
-        self.assertEqual(alb._extendors[IFoo], [IFoo])
+        self.assertEqual(alb._extendors[IFoo], [IFoo, IBar])
         self.assertEqual(alb._extendors[IBar], [IBar])
         self.assertEqual(sorted(alb._extendors[Interface]),
                          sorted([IFoo, IBar]))
@@ -847,14 +847,14 @@ def test_init_extendors_after_registry_update(self):
         from zope.interface import Interface
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry()
         alb = self._makeOne(registry)
         registry._provided = [IFoo, IBar]
         alb.init_extendors()
         self.assertEqual(sorted(alb._extendors.keys()),
                          sorted([IBar, IFoo, Interface]))
-        self.assertEqual(alb._extendors[IFoo], [IFoo])
+        self.assertEqual(alb._extendors[IFoo], [IFoo, IBar])
         self.assertEqual(alb._extendors[IBar], [IBar])
         self.assertEqual(sorted(alb._extendors[Interface]),
                          sorted([IFoo, IBar]))
@@ -863,14 +863,14 @@ def test_add_extendor(self):
         from zope.interface import Interface
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry()
         alb = self._makeOne(registry)
         alb.add_extendor(IFoo)
         alb.add_extendor(IBar)
         self.assertEqual(sorted(alb._extendors.keys()),
                          sorted([IBar, IFoo, Interface]))
-        self.assertEqual(alb._extendors[IFoo], [IFoo])
+        self.assertEqual(alb._extendors[IFoo], [IFoo, IBar])
         self.assertEqual(alb._extendors[IBar], [IBar])
         self.assertEqual(sorted(alb._extendors[Interface]),
                          sorted([IFoo, IBar]))
@@ -879,13 +879,13 @@ def test_remove_extendor(self):
         from zope.interface import Interface
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         alb = self._makeOne(registry)
         alb.remove_extendor(IFoo)
         self.assertEqual(sorted(alb._extendors.keys()),
                          sorted([IFoo, IBar, Interface]))
-        self.assertEqual(alb._extendors[IFoo], [])
+        self.assertEqual(alb._extendors[IFoo], [IBar])
         self.assertEqual(alb._extendors[IBar], [IBar])
         self.assertEqual(sorted(alb._extendors[Interface]),
                          sorted([IBar]))
@@ -895,7 +895,7 @@ def test_remove_extendor(self):
     def test__uncached_lookup_empty_ro(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry()
         alb = self._makeOne(registry)
         result = alb._uncached_lookup((IFoo,), IBar)
@@ -906,7 +906,7 @@ def test__uncached_lookup_empty_ro(self):
     def test__uncached_lookup_order_miss(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
         registry.ro.append(subr)
@@ -917,7 +917,7 @@ def test__uncached_lookup_order_miss(self):
     def test__uncached_lookup_extendors_miss(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry()
         subr = self._makeSubregistry()
         subr._adapters = [{}, {}] #utilities, single adapters
@@ -930,7 +930,7 @@ def test__uncached_lookup_extendors_miss(self):
     def test__uncached_lookup_components_miss_wrong_iface(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         IQux = InterfaceClass('IQux')
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
@@ -949,7 +949,7 @@ def test__uncached_lookup_components_miss_wrong_iface(self):
     def test__uncached_lookup_components_miss_wrong_name(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
 
@@ -968,7 +968,7 @@ def test__uncached_lookup_components_miss_wrong_name(self):
     def test__uncached_lookup_simple_hit(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
         _expected = object()
@@ -985,7 +985,7 @@ def test__uncached_lookup_simple_hit(self):
     def test__uncached_lookup_repeated_hit(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
         _expected = object()
@@ -1005,7 +1005,7 @@ def test_queryMultiAdaptor_lookup_miss(self):
         from zope.interface.declarations import implementer
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         @implementer(IFoo)
         class Foo(object):
             pass
@@ -1051,7 +1051,7 @@ def test_queryMultiAdaptor_factory_miss(self):
         from zope.interface.declarations import implementer
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         @implementer(IFoo)
         class Foo(object):
             pass
@@ -1080,7 +1080,7 @@ def test_queryMultiAdaptor_factory_hit(self):
         from zope.interface.declarations import implementer
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         @implementer(IFoo)
         class Foo(object):
             pass
@@ -1131,7 +1131,7 @@ def factory(*args):
     def test__uncached_lookupAll_empty_ro(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry()
         alb = self._makeOne(registry)
         result = alb._uncached_lookupAll((IFoo,), IBar)
@@ -1142,7 +1142,7 @@ def test__uncached_lookupAll_empty_ro(self):
     def test__uncached_lookupAll_order_miss(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
         registry.ro.append(subr)
@@ -1154,7 +1154,7 @@ def test__uncached_lookupAll_order_miss(self):
     def test__uncached_lookupAll_extendors_miss(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry()
         subr = self._makeSubregistry()
         subr._adapters = [{}, {}] #utilities, single adapters
@@ -1167,7 +1167,7 @@ def test__uncached_lookupAll_extendors_miss(self):
     def test__uncached_lookupAll_components_miss(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         IQux = InterfaceClass('IQux')
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
@@ -1185,7 +1185,7 @@ def test__uncached_lookupAll_components_miss(self):
     def test__uncached_lookupAll_simple_hit(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
         _expected = object()
@@ -1203,7 +1203,7 @@ def test__uncached_lookupAll_simple_hit(self):
     def test_names(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
         _expected = object()
@@ -1222,7 +1222,7 @@ def test_names(self):
     def test__uncached_subscriptions_empty_ro(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry()
         alb = self._makeOne(registry)
         result = alb._uncached_subscriptions((IFoo,), IBar)
@@ -1233,7 +1233,7 @@ def test__uncached_subscriptions_empty_ro(self):
     def test__uncached_subscriptions_order_miss(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
         registry.ro.append(subr)
@@ -1245,7 +1245,7 @@ def test__uncached_subscriptions_order_miss(self):
     def test__uncached_subscriptions_extendors_miss(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry()
         subr = self._makeSubregistry()
         subr._subscribers = [{}, {}] #utilities, single adapters
@@ -1258,7 +1258,7 @@ def test__uncached_subscriptions_extendors_miss(self):
     def test__uncached_subscriptions_components_miss_wrong_iface(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         IQux = InterfaceClass('IQux')
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
@@ -1276,7 +1276,7 @@ def test__uncached_subscriptions_components_miss_wrong_iface(self):
     def test__uncached_subscriptions_components_miss_wrong_name(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
         wrongname = object()
@@ -1293,7 +1293,7 @@ def test__uncached_subscriptions_components_miss_wrong_name(self):
     def test__uncached_subscriptions_simple_hit(self):
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         registry = self._makeRegistry(IFoo, IBar)
         subr = self._makeSubregistry()
         class Foo(object):
@@ -1314,7 +1314,7 @@ def test_subscribers_wo_provided(self):
         from zope.interface.declarations import implementer
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         @implementer(IFoo)
         class Foo(object):
             pass
@@ -1343,7 +1343,7 @@ def test_subscribers_w_provided(self):
         from zope.interface.declarations import implementer
         from zope.interface.interface import InterfaceClass
         IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar', IFoo)
+        IBar = InterfaceClass('IBar', (IFoo,))
         @implementer(IFoo)
         class Foo(object):
             pass
diff --git a/src/zope/interface/tests/test_declarations.py b/src/zope/interface/tests/test_declarations.py
index 5d7272a9..83815d7e 100644
--- a/src/zope/interface/tests/test_declarations.py
+++ b/src/zope/interface/tests/test_declarations.py
@@ -864,25 +864,30 @@ class Foo(object):
     def test_w_existing_Implements_w_bases(self):
         from zope.interface.declarations import Implements
         from zope.interface.interface import InterfaceClass
-        IFoo = InterfaceClass('IFoo')
-        IBar = InterfaceClass('IBar')
-        IBaz = InterfaceClass('IBaz', IFoo)
-        b_impl = Implements(IBaz)
-        impl = Implements(IFoo)
-        impl.declared = (IFoo,)
-        class Base1(object):
-            __implemented__ = b_impl
-        class Base2(object):
-            __implemented__ = b_impl
-        class Foo(Base1, Base2):
-            __implemented__ = impl
-        impl.inherit = Foo
-        self._callFUT(Foo, IBar)
+        IRoot = InterfaceClass('IRoot')
+        ISecondRoot = InterfaceClass('ISecondRoot')
+        IExtendsRoot = InterfaceClass('IExtendsRoot', (IRoot,))
+
+        impl_root = Implements.named('Root', IRoot)
+        impl_root.declared = (IRoot,)
+
+        class Root1(object):
+            __implemented__ = impl_root
+        class Root2(object):
+            __implemented__ = impl_root
+
+        impl_extends_root = Implements.named('ExtendsRoot1', IExtendsRoot)
+        impl_extends_root.declared = (IExtendsRoot,)
+        class ExtendsRoot(Root1, Root2):
+            __implemented__ = impl_extends_root
+        impl_extends_root.inherit = ExtendsRoot
+
+        self._callFUT(ExtendsRoot, ISecondRoot)
         # Same spec, now different values
-        self.assertTrue(Foo.__implemented__ is impl)
-        self.assertEqual(impl.inherit, Foo)
-        self.assertEqual(impl.declared, (IFoo, IBar,))
-        self.assertEqual(impl.__bases__, (IFoo, IBar, b_impl))
+        self.assertIs(ExtendsRoot.__implemented__, impl_extends_root)
+        self.assertEqual(impl_extends_root.inherit, ExtendsRoot)
+        self.assertEqual(impl_extends_root.declared, (IExtendsRoot, ISecondRoot,))
+        self.assertEqual(impl_extends_root.__bases__, (IExtendsRoot, ISecondRoot, impl_root))
 
 
 class Test__implements_advice(unittest.TestCase):
diff --git a/src/zope/interface/tests/test_interface.py b/src/zope/interface/tests/test_interface.py
index 21003407..4bbed1a7 100644
--- a/src/zope/interface/tests/test_interface.py
+++ b/src/zope/interface/tests/test_interface.py
@@ -1318,9 +1318,9 @@ def testInterfaceExtendsInterface(self):
 
         new = Interface.__class__
         FunInterface = new('FunInterface')
-        BarInterface = new('BarInterface', [FunInterface])
+        BarInterface = new('BarInterface', (FunInterface,))
         BobInterface = new('BobInterface')
-        BazInterface = new('BazInterface', [BobInterface, BarInterface])
+        BazInterface = new('BazInterface', (BobInterface, BarInterface,))
 
         self.assertTrue(BazInterface.extends(BobInterface))
         self.assertTrue(BazInterface.extends(BarInterface))
@@ -2161,6 +2161,128 @@ class C(object):
         finally:
             adapter_hooks[:] = old_adapter_hooks
 
+    def test___call___w_overridden_adapt(self):
+        from zope.interface import Interface
+        from zope.interface import interfacemethod
+        from zope.interface import implementer
+
+        class I(Interface):
+
+            @interfacemethod
+            def __adapt__(self, obj):
+                return 42
+
+        @implementer(I)
+        class O(object):
+            pass
+
+        self.assertEqual(42, I(object()))
+        # __adapt__ supercedes providedBy() if defined.
+        self.assertEqual(42, I(O()))
+
+    def test___call___w_overridden_adapt_call_super(self):
+        import sys
+        from zope.interface import Interface
+        from zope.interface import interfacemethod
+        from zope.interface import implementer
+
+        class I(Interface):
+
+            @interfacemethod
+            def __adapt__(self, obj):
+                if not self.providedBy(obj):
+                    return 42
+                if sys.version_info[:2] > (3, 5):
+                    # Python 3.5 raises 'RuntimeError: super() __class__ is not a type'
+                    return super().__adapt__(obj)
+
+                return super(type(I), self).__adapt__(obj)
+
+        @implementer(I)
+        class O(object):
+            pass
+
+        self.assertEqual(42, I(object()))
+        o = O()
+        self.assertIs(o, I(o))
+
+    def test___adapt___as_method_and_implementation(self):
+        from zope.interface import Interface
+        from zope.interface import interfacemethod
+
+        class I(Interface):
+            @interfacemethod
+            def __adapt__(self, obj):
+                return 42
+
+            def __adapt__(to_adapt):
+                "This is a protocol"
+
+        self.assertEqual(42, I(object()))
+        self.assertEqual(I['__adapt__'].getSignatureString(), '(to_adapt)')
+
+    def test___adapt__inheritance_and_type(self):
+        from zope.interface import Interface
+        from zope.interface import interfacemethod
+
+        class IRoot(Interface):
+            """Root"""
+
+        class IWithAdapt(IRoot):
+            @interfacemethod
+            def __adapt__(self, obj):
+                return 42
+
+        class IOther(IRoot):
+            """Second branch"""
+
+        class IUnrelated(Interface):
+            """Unrelated"""
+
+        class IDerivedAdapt(IUnrelated, IWithAdapt, IOther):
+            """Inherits an adapt"""
+            # Order of "inheritance" matters here.
+
+        class IDerived2Adapt(IDerivedAdapt):
+            """Overrides an inherited custom adapt."""
+            @interfacemethod
+            def __adapt__(self, obj):
+                return 24
+
+        self.assertEqual(42, IDerivedAdapt(object()))
+        for iface in IRoot, IWithAdapt, IOther, IUnrelated, IDerivedAdapt:
+            self.assertEqual(__name__, iface.__module__)
+
+        for iface in IRoot, IOther, IUnrelated:
+            self.assertEqual(type(IRoot), type(Interface))
+
+        # But things that implemented __adapt__ got a new type
+        self.assertNotEqual(type(Interface), type(IWithAdapt))
+        self.assertEqual(type(IWithAdapt), type(IDerivedAdapt))
+        self.assertIsInstance(IWithAdapt, type(Interface))
+
+        self.assertEqual(24, IDerived2Adapt(object()))
+        self.assertNotEqual(type(IDerived2Adapt), type(IDerivedAdapt))
+        self.assertIsInstance(IDerived2Adapt, type(IDerivedAdapt))
+
+    def test_interfacemethod_is_general(self):
+        from zope.interface import Interface
+        from zope.interface import interfacemethod
+
+        class I(Interface):
+
+            @interfacemethod
+            def __call__(self, obj):
+                """Replace an existing method"""
+                return 42
+
+            @interfacemethod
+            def this_is_new(self):
+                return 42
+
+        self.assertEqual(I(self), 42)
+        self.assertEqual(I.this_is_new(), 42)
+
 
 class AttributeTests(ElementTests):