diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index a7fe1898a..204aaa43a 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -1469,9 +1469,17 @@ struct enum_base {
                 },                                                                     \
                 is_method(m_base))
 
+        #define PYBIND11_ENUM_OP_CONV_LHS(op, expr)                                    \
+            m_base.attr(op) = cpp_function(                                            \
+                [](object a_, object b) {                                              \
+                    int_ a(a_);                                                        \
+                    return expr;                                                       \
+                },                                                                     \
+                is_method(m_base))
+
         if (is_convertible) {
-            PYBIND11_ENUM_OP_CONV("__eq__", !b.is_none() &&  a.equal(b));
-            PYBIND11_ENUM_OP_CONV("__ne__",  b.is_none() || !a.equal(b));
+            PYBIND11_ENUM_OP_CONV_LHS("__eq__", !b.is_none() &&  a.equal(b));
+            PYBIND11_ENUM_OP_CONV_LHS("__ne__",  b.is_none() || !a.equal(b));
 
             if (is_arithmetic) {
                 PYBIND11_ENUM_OP_CONV("__lt__",   a <  b);
@@ -1501,6 +1509,7 @@ struct enum_base {
             }
         }
 
+        #undef PYBIND11_ENUM_OP_CONV_LHS
         #undef PYBIND11_ENUM_OP_CONV
         #undef PYBIND11_ENUM_OP_STRICT
 
diff --git a/tests/test_enum.cpp b/tests/test_enum.cpp
index 498a00e16..315308920 100644
--- a/tests/test_enum.cpp
+++ b/tests/test_enum.cpp
@@ -13,11 +13,13 @@ TEST_SUBMODULE(enums, m) {
     // test_unscoped_enum
     enum UnscopedEnum {
         EOne = 1,
-        ETwo
+        ETwo,
+        EThree
     };
     py::enum_<UnscopedEnum>(m, "UnscopedEnum", py::arithmetic(), "An unscoped enumeration")
         .value("EOne", EOne, "Docstring for EOne")
         .value("ETwo", ETwo, "Docstring for ETwo")
+        .value("EThree", EThree, "Docstring for EThree")
         .export_values();
 
     // test_scoped_enum
diff --git a/tests/test_enum.py b/tests/test_enum.py
index 2f119a3a9..7fe9b618d 100644
--- a/tests/test_enum.py
+++ b/tests/test_enum.py
@@ -21,7 +21,7 @@ def test_unscoped_enum():
 
     # __members__ property
     assert m.UnscopedEnum.__members__ == \
-        {"EOne": m.UnscopedEnum.EOne, "ETwo": m.UnscopedEnum.ETwo}
+        {"EOne": m.UnscopedEnum.EOne, "ETwo": m.UnscopedEnum.ETwo, "EThree": m.UnscopedEnum.EThree}
     # __members__ readonly
     with pytest.raises(AttributeError):
         m.UnscopedEnum.__members__ = {}
@@ -29,23 +29,18 @@ def test_unscoped_enum():
     foo = m.UnscopedEnum.__members__
     foo["bar"] = "baz"
     assert m.UnscopedEnum.__members__ == \
-        {"EOne": m.UnscopedEnum.EOne, "ETwo": m.UnscopedEnum.ETwo}
+        {"EOne": m.UnscopedEnum.EOne, "ETwo": m.UnscopedEnum.ETwo, "EThree": m.UnscopedEnum.EThree}
 
-    assert m.UnscopedEnum.__doc__ == \
-        '''An unscoped enumeration
+    for docstring_line in '''An unscoped enumeration
 
 Members:
 
   EOne : Docstring for EOne
 
-  ETwo : Docstring for ETwo''' or m.UnscopedEnum.__doc__ == \
-        '''An unscoped enumeration
-
-Members:
-
   ETwo : Docstring for ETwo
 
-  EOne : Docstring for EOne'''
+  EThree : Docstring for EThree'''.split('\n'):
+        assert docstring_line in m.UnscopedEnum.__doc__
 
     # Unscoped enums will accept ==/!= int comparisons
     y = m.UnscopedEnum.ETwo
@@ -53,6 +48,38 @@ Members:
     assert 2 == y
     assert y != 3
     assert 3 != y
+    # Compare with None
+    assert (y != None)  # noqa: E711
+    assert not (y == None)  # noqa: E711
+    # Compare with an object
+    assert (y != object())
+    assert not (y == object())
+    # Compare with string
+    assert y != "2"
+    assert "2" != y
+    assert not ("2" == y)
+    assert not (y == "2")
+
+    with pytest.raises(TypeError):
+        y < object()
+
+    with pytest.raises(TypeError):
+        y <= object()
+
+    with pytest.raises(TypeError):
+        y > object()
+
+    with pytest.raises(TypeError):
+        y >= object()
+
+    with pytest.raises(TypeError):
+        y | object()
+
+    with pytest.raises(TypeError):
+        y & object()
+
+    with pytest.raises(TypeError):
+        y ^ object()
 
     assert int(m.UnscopedEnum.ETwo) == 2
     assert str(m.UnscopedEnum(2)) == "UnscopedEnum.ETwo"
@@ -71,6 +98,11 @@ Members:
     assert not (m.UnscopedEnum.ETwo < m.UnscopedEnum.EOne)
     assert not (2 < m.UnscopedEnum.EOne)
 
+    # arithmetic
+    assert m.UnscopedEnum.EOne & m.UnscopedEnum.EThree == m.UnscopedEnum.EOne
+    assert m.UnscopedEnum.EOne | m.UnscopedEnum.ETwo == m.UnscopedEnum.EThree
+    assert m.UnscopedEnum.EOne ^ m.UnscopedEnum.EThree == m.UnscopedEnum.ETwo
+
 
 def test_scoped_enum():
     assert m.test_scoped_enum(m.ScopedEnum.Three) == "ScopedEnum::Three"
@@ -82,6 +114,12 @@ def test_scoped_enum():
     assert not 3 == z
     assert z != 3
     assert 3 != z
+    # Compare with None
+    assert (z != None)  # noqa: E711
+    assert not (z == None)  # noqa: E711
+    # Compare with an object
+    assert (z != object())
+    assert not (z == object())
     # Scoped enums will *NOT* accept >, <, >= and <= int comparisons (Will throw exceptions)
     with pytest.raises(TypeError):
         z > 3