diff --git a/clld/db/models/parameter.py b/clld/db/models/parameter.py
index cb81fd72..a0513029 100644
--- a/clld/db/models/parameter.py
+++ b/clld/db/models/parameter.py
@@ -41,10 +41,11 @@ class DomainElement(Base,
     """DomainElements can be used to model controlled lists of values for a Parameter."""
 
     __table_args__ = (
-        UniqueConstraint('name', 'parameter_pk'),
-        UniqueConstraint('number', 'parameter_pk'))
+        UniqueConstraint('parameter_pk', 'name'),
+        UniqueConstraint('parameter_pk', 'number'),
+    )
 
-    parameter_pk = Column(Integer, ForeignKey('parameter.pk'))
+    parameter_pk = Column(Integer, ForeignKey('parameter.pk'), nullable=False)
 
     number = Column(Integer, doc='numerical value of the domain element')
     """the number is used to sort domain elements within the domain of one parameter"""
diff --git a/clld/db/models/unit.py b/clld/db/models/unit.py
index c30174b5..98b256c1 100644
--- a/clld/db/models/unit.py
+++ b/clld/db/models/unit.py
@@ -1,6 +1,6 @@
 from __future__ import unicode_literals, print_function, division, absolute_import
 
-from sqlalchemy import Column, Integer, ForeignKey
+from sqlalchemy import Column, Integer, ForeignKey, UniqueConstraint
 from sqlalchemy.orm import relationship
 
 from zope.interface import implementer
@@ -32,11 +32,12 @@ class Unit(Base,
            IdNameDescriptionMixin,
            HasDataMixin,
            HasFilesMixin):
-
     """A linguistic unit of a language."""
 
-    language_pk = Column(Integer, ForeignKey('language.pk'))
-    language = relationship(Language)
+    __table_args__ = (UniqueConstraint('language_pk', 'id'),)
+
+    language_pk = Column(Integer, ForeignKey('language.pk'), nullable=False)
+    language = relationship(Language, innerjoin=True)
 
     def __solr__(self, req):
         return _add_solr_language_info(Base.__solr__(self, req), self)
diff --git a/clld/db/models/unitparameter.py b/clld/db/models/unitparameter.py
index e90f5810..580138fb 100644
--- a/clld/db/models/unitparameter.py
+++ b/clld/db/models/unitparameter.py
@@ -1,6 +1,6 @@
 from __future__ import unicode_literals, print_function, division, absolute_import
 
-from sqlalchemy import Column, Integer, ForeignKey
+from sqlalchemy import Column, Integer, ForeignKey, UniqueConstraint
 from sqlalchemy.orm import relationship
 
 from zope.interface import implementer
@@ -32,7 +32,12 @@ class UnitDomainElement(Base,
 
     """Domain element for the domain of a UnitParameter."""
 
-    unitparameter_pk = Column(Integer, ForeignKey('unitparameter.pk'))
+    __table_args__ = (
+        UniqueConstraint('unitparameter_pk', 'name'),
+        UniqueConstraint('unitparameter_pk', 'ord'),
+    )
+
+    unitparameter_pk = Column(Integer, ForeignKey('unitparameter.pk'), nullable=False)
     ord = Column(Integer)
 
     def url(self, request):
diff --git a/clld/db/schema_migrations/update_assoc_tables.py b/clld/db/schema_migrations/update_unique_null.py
similarity index 92%
rename from clld/db/schema_migrations/update_assoc_tables.py
rename to clld/db/schema_migrations/update_unique_null.py
index e36ebc3e..70da656b 100644
--- a/clld/db/schema_migrations/update_assoc_tables.py
+++ b/clld/db/schema_migrations/update_unique_null.py
@@ -1,9 +1,4 @@
-# update_assoc_tables.py - adapt unique and nullable
-
-# TODO: DomainElement: reverse UNIQUE(name, parameter_pk)?, parameter_pk NOT NULL?
-# TODO: LanguageSource: orm.relationships missing?
-# TODO: Unit: language_pk NOT_NULL, innerjoin=True?
-# TODO: UnitDomainElement: add UNIQUE(unitparameter_pk, name)?, unitparameter_pk NOT NULL?
+# update_unique_null.py - adapt composite unique constraints and nullables
 
 from __future__ import unicode_literals
 
@@ -30,6 +25,12 @@
     ('contributionreference',
         ['contribution_pk', 'source_pk', 'description'],
         ['description']),
+    ('domainelement',
+        ['parameter_pk', 'name'],
+        ['name']),
+    ('domainelement',
+        ['parameter_pk', 'number'],
+        ['number']),
     ('editor',
         ['dataset_pk', 'contributor_pk'], []),
     ('languageidentifier',
@@ -39,6 +40,15 @@
     ('sentencereference',
         ['sentence_pk', 'source_pk', 'description'],
         ['description']),
+    ('unit',
+        ['language_pk', 'id'],  # FIXME: or rather name?
+        ['id']),
+    ('unitdomainelement',
+        ['unitparameter_pk', 'name'],
+        ['name']),
+    ('unitdomainelement',
+        ['unitparameter_pk', 'ord'],
+        ['ord']),
     ('unitvalue',  # NOTE: <unit, unitparameter, contribution> can have multiple values and also multiple unitdomainelements
         ['unit_pk', 'unitparameter_pk', 'contribution_pk', 'name', 'unitdomainelement_pk'],
         ['contribution_pk', 'name', 'unitdomainelement_pk']),