diff --git a/jedi/inference/value/instance.py b/jedi/inference/value/instance.py
index 1e368d34..a6b6931a 100644
--- a/jedi/inference/value/instance.py
+++ b/jedi/inference/value/instance.py
@@ -19,7 +19,7 @@ from jedi.inference.value.function import \
     BaseFunctionExecutionContext, FunctionExecutionContext
 from jedi.inference.value.klass import ClassFilter
 from jedi.inference.value.dynamic_arrays import get_dynamic_array_instance
-from jedi.parser_utils import function_is_static_method
+from jedi.parser_utils import function_is_staticmethod, function_is_classmethod
 
 
 class InstanceExecutedParamName(ParamName):
@@ -41,9 +41,19 @@ class AnonymousMethodExecutionFilter(AnonymousFunctionExecutionFilter):
         self._instance = instance
 
     def _convert_param(self, param, name):
-        if param.position_index == 0 \
-                and not function_is_static_method(self._function_value.tree_node):
-            return InstanceExecutedParamName(self._instance, self._function_value, name)
+        if param.position_index == 0:
+            if function_is_classmethod(self._function_value.tree_node):
+                return InstanceExecutedParamName(
+                    self._instance.py__class__(),
+                    self._function_value,
+                    name
+                )
+            elif not function_is_staticmethod(self._function_value.tree_node):
+                return InstanceExecutedParamName(
+                    self._instance,
+                    self._function_value,
+                    name
+                )
         return super(AnonymousMethodExecutionFilter, self)._convert_param(param, name)
 
 
diff --git a/jedi/parser_utils.py b/jedi/parser_utils.py
index 9912c9f9..f8537858 100644
--- a/jedi/parser_utils.py
+++ b/jedi/parser_utils.py
@@ -297,9 +297,21 @@ def get_string_quote(leaf):
     return re.match(r'\w*("""|\'{3}|"|\')', leaf.value).group(1)
 
 
-def function_is_static_method(function_node):
-    for decorator in function_node.get_decorators():
-        dotted_name = decorator.children[1]
-        if dotted_name.get_code() == 'staticmethod':
-            return True
-    return False
+def _function_is_x_method(method_name):
+    def wrapper(function_node):
+        """
+        This is a heuristic. It will not hold ALL the times, but it will be
+        correct pretty much for anyone that doesn't try to beat it.
+        staticmethod/classmethod are builtins and unless overwritten, this will
+        be correct.
+        """
+        for decorator in function_node.get_decorators():
+            dotted_name = decorator.children[1]
+            if dotted_name.get_code() == method_name:
+                return True
+        return False
+    return wrapper
+
+
+function_is_staticmethod = _function_is_x_method('staticmethod')
+function_is_classmethod = _function_is_x_method('classmethod')
diff --git a/test/completion/stdlib.py b/test/completion/stdlib.py
index 10573377..636b66fb 100644
--- a/test/completion/stdlib.py
+++ b/test/completion/stdlib.py
@@ -318,13 +318,28 @@ class F():
         #?
         return param
 
+    @classmethod
+    def my_method_without_call(cls, param):
+        #?
+        cls.my_variable
+        #? ['my_method', 'my_method_without_call']
+        cls.my_meth
+        #?
+        return param
+
     @classmethod
     def my_method(cls, param):
-        #? []
-        param.my_method
-
+        #?
+        cls.my_variable
+        #? ['my_method', 'my_method_without_call']
+        cls.my_meth
+        #?
+        return param
 
+#? str()
 F.my_func('')
+#? str()
+F.my_method('')
 
 # -----------------
 # Unknown metaclass