diff --git a/README.md b/README.md
index 02320cc..046a972 100644
--- a/README.md
+++ b/README.md
@@ -121,20 +121,21 @@ assert mul([1, 2], [3, 4]) == [3, 8]        # list, list
 Dispatch can also be used for extending the dataclass builtin `__init__`:
 
 ```python
-@dataclass(frozen=False)
+@dataclass
 class Point:
     x: int = 0
     y: int = 0
-    
+
     @md
     def __init__(self, points: list | tuple):
-        self.x, self.y = points
+        # Call default constructor
+        self.__init__(*points)
 
     @md
     def __init__(self, points: dict):
-        self.x = points['x']
-        self.y = points['y']
-    
+        # Call default constructor
+        self.__init__(points['x'], points['y'])
+
 # Test constructors
 p0 = Point()                         # Default constructor
 assert p0 == Point(0, 0)             # Default constructor
diff --git a/runtype/dataclass.py b/runtype/dataclass.py
index c12992b..c49abdf 100644
--- a/runtype/dataclass.py
+++ b/runtype/dataclass.py
@@ -2,6 +2,7 @@
 Enhances Python's built-in dataclass, with type-checking and extra ergonomics.
 """
 
+import sys
 import random
 from copy import copy
 import dataclasses
@@ -28,6 +29,7 @@ def dataclass_transform(*a, **kw):
 Skip = object()
 MAX_SAMPLE_SIZE = 16
 
+IS_PY310 = sys.version_info >= (3, 10)
 
 class NopTypeCaster(ATypeCaster):
     cache: Dict[int, Union[PythonType, type]] = {}
@@ -370,11 +372,17 @@ def __post_init__(self):
         # __init__ may have been generated by the dataclass function
         if hasattr(c, "__init__"):
             # We will add it to the dispatch
-            c.__init__ = init_dispatcher(c.__init__)
+            c.__init__ = init_dispatcher(_fix_qualname(c.__init__, cls))
         else:
             c.__init__ = init_f
     return c
 
+def _fix_qualname(f, cls):
+    if not IS_PY310:
+        # XXX Hack for old Python versions -
+        # Dataclasses generated __init__ with wrong __qualname__
+        f.__qualname__ = f"{cls.__qualname__}.{f.__name__}"
+    return f
 
 def _dataclass_getstate(self):
     return [getattr(self, f.name) for f in dataclasses.fields(self)]
diff --git a/runtype/dispatch.py b/runtype/dispatch.py
index 2472ee1..7528f5a 100644
--- a/runtype/dispatch.py
+++ b/runtype/dispatch.py
@@ -50,7 +50,7 @@ def __call__(self, func=None, *, priority=None):
                 "Must either provide a function to decorate, or set a priority"
             )
 
-        fname = func.__name__
+        fname = func.__qualname__
         try:
             tree = self.fname_to_tree[fname]
         except KeyError:
diff --git a/runtype/pytypes.py b/runtype/pytypes.py
index d532f5f..0dfde89 100644
--- a/runtype/pytypes.py
+++ b/runtype/pytypes.py
@@ -27,9 +27,6 @@
 
 
 
-py38 = sys.version_info >= (3, 8)
-
-
 class LengthMismatchError(TypeMismatchError):
     pass
 
@@ -486,21 +483,6 @@ def cast_from(self, obj):
 }
 
 
-if sys.version_info >= (3, 7):
-    origin_list = list
-    origin_dict = dict
-    origin_tuple = tuple
-    origin_set = set
-    origin_frozenset = frozenset
-else:
-    origin_list = typing.List
-    origin_dict = typing.Dict
-    origin_tuple = typing.Tuple
-    origin_set = typing.Set
-    origin_frozenset = typing.FrozenSet
-
-
-
 class ATypeCaster(ABC):
     @abstractmethod
     def to_canon(self, t: typing.Any): ...
@@ -575,19 +557,19 @@ def _to_canon(self, t):
 
         args = getattr(t, '__args__', None)
 
-        if origin is origin_list:
+        if origin is list:
             x ,= args
             return List[to_canon(x)]
-        elif origin is origin_set:
+        elif origin is set:
             x ,= args
             return Set[to_canon(x)]
-        elif origin is origin_frozenset:
+        elif origin is frozenset:
             x ,= args
             return FrozenSet[to_canon(x)]
-        elif origin is origin_dict:
+        elif origin is dict:
             k, v = args
             return Dict[to_canon(k), to_canon(v)]
-        elif origin is origin_tuple:
+        elif origin is tuple:
             if not args:
                 return Tuple
             if Ellipsis in args:
@@ -603,7 +585,7 @@ def _to_canon(self, t):
         elif origin is abc.Callable or origin is typing.Callable:
             return Callable[ProductType(to_canon(x) for x in args[:-1]), to_canon(args[-1])]
             return Callable  # TODO
-        elif py38 and origin is typing.Literal:
+        elif origin is typing.Literal:
             return OneOf(args)
         elif origin is abc.Mapping or origin is typing.Mapping:
             k, v = args
diff --git a/tests/test_basic.py b/tests/test_basic.py
index 03b923d..91e2eb2 100644
--- a/tests/test_basic.py
+++ b/tests/test_basic.py
@@ -704,6 +704,19 @@ def f(t: int):
         assert f(2) == "int"
         assert f(None) == "none"
 
+    def test_qualified_name(self):
+        md = Dispatch()
+
+        class A:
+            @md
+            def a(self, points: list):
+                ...
+
+        class B:
+            @md
+            def a(self, points: list):
+                ...
+
 
 class TestDataclass(TestCase):
     def setUp(self):