diff --git a/Lib/dataclasses.py b/Lib/dataclasses.py
index b55a497..8ab04dd 100644
--- a/Lib/dataclasses.py
+++ b/Lib/dataclasses.py
@@ -171,7 +171,11 @@
 
 # The name of an attribute on the class where we store the Field
 #  objects. Also used to check if a class is a Data Class.
-_MARKER = '__dataclass_fields__'
+_FIELDS = '__dataclass_fields__'
+
+# The name of an attribute on the class that stores the parameters to
+# @dataclass.
+_PARAMS = '__dataclass_params__'
 
 # The name of the function, that if it exists, is called at the end of
 # __init__.
@@ -192,7 +196,7 @@
 # name and type are filled in after the fact, not in __init__. They're
 #  not known at the time this class is instantiated, but it's
 #  convenient if they're available later.
-# When cls._MARKER is filled in with a list of Field objects, the name
+# When cls._FIELDS is filled in with a list of Field objects, the name
 #  and type fields will have been populated.
 class Field:
     __slots__ = ('name',
@@ -236,6 +240,32 @@
                 ')')
 
 
+class _DataclassParams:
+    __slots__ = ('init',
+                 'repr',
+                 'eq',
+                 'order',
+                 'unsafe_hash',
+                 'frozen',
+                 )
+    def __init__(self, init, repr, eq, order, unsafe_hash, frozen):
+        self.init = init
+        self.repr = repr
+        self.eq = eq
+        self.order = order
+        self.unsafe_hash = unsafe_hash
+        self.frozen = frozen
+
+    def __repr__(self):
+        return ('_DataclassParams('
+                f'init={self.init},'
+                f'repr={self.repr},'
+                f'eq={self.eq},'
+                f'order={self.order},'
+                f'unsafe_hash={self.unsafe_hash},'
+                f'frozen={self.frozen}'
+                ')')
+
 # This function is used instead of exposing Field creation directly,
 #  so that a type checker can be told (via overloads) that this is a
 #  function whose type depends on its parameters.
@@ -285,6 +315,7 @@
     args = ','.join(args)
     body = '\n'.join(f' {b}' for b in body)
 
+    # Compute the text of the entire function.
     txt = f'def {name}({args}){return_annotation}:\n{body}'
 
     exec(txt, globals, locals)
@@ -432,12 +463,29 @@
                        ')"'])
 
 
-def _frozen_setattr(self, name, value):
-    raise FrozenInstanceError(f'cannot assign to field {name!r}')
-
-
-def _frozen_delattr(self, name):
-    raise FrozenInstanceError(f'cannot delete field {name!r}')
+def _frozen_get_del_attr(cls, fields):
+    # XXX: globals is modified on the first call to _create_fn, then the
+    #  modified version is used in the second call.  Is this okay?
+    globals = {'cls': cls,
+              'FrozenInstanceError': FrozenInstanceError}
+    if fields:
+        fields_str = '(' + ','.join(repr(f.name) for f in fields) + ',)'
+    else:
+        # Special case for the zero-length tuple.
+        fields_str = '()'
+    return (_create_fn('__setattr__',
+                      ('self', 'name', 'value'),
+                      (f'if type(self) is cls or name in {fields_str}:',
+                        ' raise FrozenInstanceError(f"cannot assign to field {name!r}")',
+                       f'super(cls, self).__setattr__(name, value)'),
+                       globals=globals),
+            _create_fn('__delattr__',
+                      ('self', 'name'),
+                      (f'if type(self) is cls or name in {fields_str}:',
+                        ' raise FrozenInstanceError(f"cannot delete field {name!r}")',
+                       f'super(cls, self).__delattr__(name)'),
+                       globals=globals),
+            )
 
 
 def _cmp_fn(name, op, self_tuple, other_tuple):
@@ -583,23 +631,32 @@
 #  version of this table.
 
 
-def _process_class(cls, repr, eq, order, unsafe_hash, init, frozen):
+def _process_class(cls, init, repr, eq, order, unsafe_hash, frozen):
     # Now that dicts retain insertion order, there's no reason to use
     #  an ordered dict.  I am leveraging that ordering here, because
     #  derived class fields overwrite base class fields, but the order
     #  is defined by the base class, which is found first.
     fields = {}
 
+    setattr(cls, _PARAMS, _DataclassParams(init, repr, eq, order,
+                                           unsafe_hash, frozen))
+
     # Find our base classes in reverse MRO order, and exclude
     #  ourselves.  In reversed order so that more derived classes
     #  override earlier field definitions in base classes.
+    # As long as we're iterating over them, see if any are frozen.
+    any_frozen_base = False
+    has_dataclass_bases = False
     for b in cls.__mro__[-1:0:-1]:
         # Only process classes that have been processed by our
-        #  decorator.  That is, they have a _MARKER attribute.
-        base_fields = getattr(b, _MARKER, None)
+        #  decorator.  That is, they have a _FIELDS attribute.
+        base_fields = getattr(b, _FIELDS, None)
         if base_fields:
+            has_dataclass_bases = True
             for f in base_fields.values():
                 fields[f.name] = f
+            if getattr(b, _PARAMS).frozen:
+                any_frozen_base = True
 
     # Now find fields in our class.  While doing so, validate some
     #  things, and set the default values (as class attributes)
@@ -623,20 +680,21 @@
             else:
                 setattr(cls, f.name, f.default)
 
-    # We're inheriting from a frozen dataclass, but we're not frozen.
-    if cls.__setattr__ is _frozen_setattr and not frozen:
-        raise TypeError('cannot inherit non-frozen dataclass from a '
-                        'frozen one')
+    # Check rules that apply if we are derived from any dataclasses.
+    if has_dataclass_bases:
+        # Raise an exception if any of our bases are frozen, but we're not.
+        if any_frozen_base and not frozen:
+            raise TypeError('cannot inherit non-frozen dataclass from a '
+                            'frozen one')
 
-    # We're inheriting from a non-frozen dataclass, but we're frozen.
-    if (hasattr(cls, _MARKER) and cls.__setattr__ is not _frozen_setattr
-        and frozen):
-        raise TypeError('cannot inherit frozen dataclass from a '
-                        'non-frozen one')
+        # Raise an exception if we're frozen, but none of our bases are.
+        if not any_frozen_base and frozen:
+            raise TypeError('cannot inherit frozen dataclass from a '
+                            'non-frozen one')
 
-    # Remember all of the fields on our class (including bases).  This
+    # Remember all of the fields on our class (including bases).  This also
     #  marks this class as being a dataclass.
-    setattr(cls, _MARKER, fields)
+    setattr(cls, _FIELDS, fields)
 
     # Was this class defined with an explicit __hash__?  Note that if
     #  __eq__ is defined in this class, then python will automatically
@@ -704,10 +762,10 @@
                                 'functools.total_ordering')
 
     if frozen:
-        for name, fn in [('__setattr__', _frozen_setattr),
-                         ('__delattr__', _frozen_delattr)]:
-            if _set_new_attribute(cls, name, fn):
-                raise TypeError(f'Cannot overwrite attribute {name} '
+        # XXX: Which fields are frozen? InitVar? ClassVar? hashed-only?
+        for fn in _frozen_get_del_attr(cls, field_list):
+            if _set_new_attribute(cls, fn.__name__, fn):
+                raise TypeError(f'Cannot overwrite attribute {fn.__name__} '
                                 f'in class {cls.__name__}')
 
     # Decide if/how we're going to create a hash function.
@@ -759,7 +817,7 @@
     """
 
     def wrap(cls):
-        return _process_class(cls, repr, eq, order, unsafe_hash, init, frozen)
+        return _process_class(cls, init, repr, eq, order, unsafe_hash, frozen)
 
     # See if we're being called as @dataclass or @dataclass().
     if _cls is None:
@@ -779,7 +837,7 @@
 
     # Might it be worth caching this, per class?
     try:
-        fields =  getattr(class_or_instance, _MARKER)
+        fields =  getattr(class_or_instance, _FIELDS)
     except AttributeError:
         raise TypeError('must be called with a dataclass type or instance')
 
@@ -790,13 +848,13 @@
 
 def _is_dataclass_instance(obj):
     """Returns True if obj is an instance of a dataclass."""
-    return not isinstance(obj, type) and hasattr(obj, _MARKER)
+    return not isinstance(obj, type) and hasattr(obj, _FIELDS)
 
 
 def is_dataclass(obj):
     """Returns True if obj is a dataclass or an instance of a
     dataclass."""
-    return hasattr(obj, _MARKER)
+    return hasattr(obj, _FIELDS)
 
 
 def asdict(obj, *, dict_factory=dict):
@@ -953,7 +1011,7 @@
     # It's an error to have init=False fields in 'changes'.
     # If a field is not in 'changes', read its value from the provided obj.
 
-    for f in getattr(obj, _MARKER).values():
+    for f in getattr(obj, _FIELDS).values():
         if not f.init:
             # Error if this field is specified in changes.
             if f.name in changes: