diff --git a/mypy/stubgenc.py b/mypy/stubgenc.py
index 0eeb39f102dc..4b0bd4a62552 100755
--- a/mypy/stubgenc.py
+++ b/mypy/stubgenc.py
@@ -121,11 +121,11 @@ def is_c_classmethod(obj: object) -> bool:
 
 
 def is_c_property(obj: object) -> bool:
-    return inspect.isdatadescriptor(obj) and hasattr(obj, 'fget')
+    return inspect.isdatadescriptor(obj) or hasattr(obj, 'fget')
 
 
 def is_c_property_readonly(prop: Any) -> bool:
-    return prop.fset is None
+    return hasattr(prop, 'fset') and prop.fset is None
 
 
 def is_c_type(obj: object) -> bool:
@@ -287,6 +287,10 @@ def infer_prop_type(docstr: Optional[str]) -> Optional[str]:
         else:
             return None
 
+    # Ignore special properties/attributes.
+    if name.startswith('__') and name.endswith('__'):
+        return
+
     inferred = infer_prop_type(getattr(obj, '__doc__', None))
     if not inferred:
         fget = getattr(obj, 'fget', None)
diff --git a/mypy/test/teststubgen.py b/mypy/test/teststubgen.py
index c999e3c82643..625ec3f30685 100644
--- a/mypy/test/teststubgen.py
+++ b/mypy/test/teststubgen.py
@@ -20,7 +20,8 @@
 )
 from mypy.stubutil import walk_packages, remove_misplaced_type_comments, common_dir_prefix
 from mypy.stubgenc import (
-    generate_c_type_stub, infer_method_sig, generate_c_function_stub, generate_c_property_stub
+    generate_c_type_stub, infer_method_sig, generate_c_function_stub, generate_c_property_stub,
+    is_c_property_readonly
 )
 from mypy.stubdoc import (
     parse_signature, parse_all_signatures, build_signature, find_unique_signatures,
@@ -868,9 +869,34 @@ def get_attribute(self) -> None:
                 pass
             attribute = property(get_attribute, doc="")
 
-        output: List[str] = []
-        generate_c_property_stub('attribute', TestClass.attribute, [], [], output, readonly=True)
-        assert_equal(output, ['@property', 'def attribute(self) -> str: ...'])
+        readwrite_properties: List[str] = []
+        readonly_properties: List[str] = []
+        generate_c_property_stub('attribute', TestClass.attribute, [],
+                                 readwrite_properties, readonly_properties,
+                                 is_c_property_readonly(TestClass.attribute))
+        assert_equal(readwrite_properties, [])
+        assert_equal(readonly_properties, ['@property', 'def attribute(self) -> str: ...'])
+
+    def test_generate_c_property_with_rw_property(self) -> None:
+        class TestClass:
+            def __init__(self) -> None:
+                self._attribute = 0
+
+            @property
+            def attribute(self) -> int:
+                return self._attribute
+
+            @attribute.setter
+            def attribute(self, value: int) -> None:
+                self._attribute = value
+
+        readwrite_properties: List[str] = []
+        readonly_properties: List[str] = []
+        generate_c_property_stub("attribute", type(TestClass.attribute), [],
+                                 readwrite_properties, readonly_properties,
+                                 is_c_property_readonly(TestClass.attribute))
+        assert_equal(readwrite_properties, ['attribute: Any'])
+        assert_equal(readonly_properties, [])
 
     def test_generate_c_type_with_single_arg_generic(self) -> None:
         class TestClass:
diff --git a/test-data/stubgen/pybind11_mypy_demo/basics.pyi b/test-data/stubgen/pybind11_mypy_demo/basics.pyi
index 7c83f4ad2256..99093fd6087a 100644
--- a/test-data/stubgen/pybind11_mypy_demo/basics.pyi
+++ b/test-data/stubgen/pybind11_mypy_demo/basics.pyi
@@ -5,8 +5,6 @@ PI: float
 
 class Point:
     class AngleUnit:
-        __doc__: ClassVar[str] = ...  # read-only
-        __members__: ClassVar[dict] = ...  # read-only
         __entries: ClassVar[dict] = ...
         degree: ClassVar[Point.AngleUnit] = ...
         radian: ClassVar[Point.AngleUnit] = ...
@@ -22,8 +20,6 @@ class Point:
         def name(self) -> str: ...
 
     class LengthUnit:
-        __doc__: ClassVar[str] = ...  # read-only
-        __members__: ClassVar[dict] = ...  # read-only
         __entries: ClassVar[dict] = ...
         inch: ClassVar[Point.LengthUnit] = ...
         mm: ClassVar[Point.LengthUnit] = ...