diff --git a/equinox/_jit.py b/equinox/_jit.py
index 633fe99a..997c6f2e 100644
--- a/equinox/_jit.py
+++ b/equinox/_jit.py
@@ -92,8 +92,9 @@ class XlaRuntimeError(Exception):
 def _modify_traceback(e: Exception):
     # Remove JAX's UnfilteredStackTrace, with its huge error messages.
     e.__cause__ = None
-    # Remove _JitWrapper.__call__ and _JitWrapper._call from the traceback
-    tb = e.__traceback__ = e.__traceback__.tb_next.tb_next  # pyright: ignore
+    # Remove _JitWrapper.__call__ and _JitWrapper._call and Method.__call__ from the
+    # traceback
+    tb = e.__traceback__ = e.__traceback__.tb_next.tb_next.tb_next  # pyright: ignore
     try:
         # See https://github.com/google/jax/blob/69cd3ebe99ce12a9f22e50009c00803a095737c7/jax/_src/traceback_util.py#L190  # noqa: E501
         jax.lib.xla_extension.replace_thread_exc_traceback(tb)  # pyright: ignore
diff --git a/equinox/_module.py b/equinox/_module.py
index 7293fecc..69b26d77 100644
--- a/equinox/_module.py
+++ b/equinox/_module.py
@@ -1,6 +1,7 @@
 import dataclasses
 import functools as ft
 import inspect
+import types
 import weakref
 from collections.abc import Callable
 from typing import Any, cast, TYPE_CHECKING, TypeVar, Union
@@ -100,8 +101,7 @@ def __init__(self, method):
     def __get__(self, instance, owner):
         if instance is None:
             return self.method
-        _method = ft.wraps(self.method)(jtu.Partial(self.method, instance))
-        delattr(_method, "__wrapped__")
+        _method = module_update_wrapper(BoundMethod(self.method, instance), self.method)
         return _method
 
 
@@ -540,3 +540,15 @@ def __call__(self, *args, **kwargs):
         The result of the wrapped function.
         """
         return self.func(*self.args, *args, **kwargs, **self.keywords)
+
+
+class BoundMethod(Module):
+    func: types.FunctionType = field(static=True)
+    instance: Module
+
+    def __call__(self, *args, **kwargs):
+        return self.func(self.instance, *args, **kwargs)
+
+    @property
+    def __wrapped__(self):
+        return self.func.__get__(self.instance, type(self.instance))  # pyright: ignore
diff --git a/tests/test_enum.py b/tests/test_enum.py
index 71e37af6..305ea9d6 100644
--- a/tests/test_enum.py
+++ b/tests/test_enum.py
@@ -2,6 +2,7 @@
 import jax.numpy as jnp
 import pytest
 
+import equinox as eqx
 import equinox.internal as eqxi
 
 from .helpers import shaped_allclose
@@ -245,11 +246,11 @@ class A(eqxi.Enumeration):
 
     token = jnp.array(True)
     A.a.error_if(token, False)
-    jax.jit(A.a.error_if)(token, False)
+    eqx.filter_jit(A.a.error_if)(token, False)
     with pytest.raises(Exception):
         A.a.error_if(token, True)
     with pytest.raises(Exception):
-        jax.jit(A.a.error_if)(token, True)
+        eqx.filter_jit(A.a.error_if)(token, True)
 
 
 def test_compile_time_eval():
diff --git a/tests/test_errors.py b/tests/test_errors.py
index 18354973..031f2cd7 100644
--- a/tests/test_errors.py
+++ b/tests/test_errors.py
@@ -181,11 +181,13 @@ def _raises():
         while tb is not None:
             code_stack.append(tb.tb_frame.f_code)
             tb = tb.tb_next
-        assert len(code_stack) == 3
-        one, two, three = code_stack
+        assert len(code_stack) == 4
+        one, two, three, four = code_stack
         assert one.co_filename.endswith("test_errors.py")
         assert one.co_name == "test_traceback_runtime_custom"
         assert two.co_filename.endswith("equinox/_jit.py")
         assert two.co_name == "__call__"
-        assert three.co_filename.endswith("equinox/_jit.py")
-        assert three.co_name == "_call"
+        assert three.co_filename.endswith("equinox/_module.py")
+        assert three.co_name == "__call__"
+        assert four.co_filename.endswith("equinox/_jit.py")
+        assert four.co_name == "_call"
diff --git a/tests/test_module.py b/tests/test_module.py
index 5a9ed129..35c0e725 100644
--- a/tests/test_module.py
+++ b/tests/test_module.py
@@ -183,13 +183,29 @@ def f(self, b):
             return self.a + b
 
     m = MyModule(13)
-    assert isinstance(m.f, jtu.Partial)
+    assert isinstance(m.f, eqx.Module)
     flat, treedef = jtu.tree_flatten(m.f)
     assert len(flat) == 1
     assert flat[0] == 13
     assert jtu.tree_unflatten(treedef, flat)(2) == 15
 
 
+def test_eq_method():
+    # Expected behaviour from non-Module methods
+    class A:
+        def f(self):
+            pass
+
+    a = A()
+    assert a.f == a.f
+
+    class B(eqx.Module):
+        def f(self):
+            pass
+
+    assert B().f == B().f
+
+
 def test_init_subclass():
     ran = []