diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index 6b7179e3..de772e78 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -38,6 +38,7 @@ jobs:
           name: coverage-data-${{ matrix.python-version }}
           path: .coverage.*
           if-no-files-found: ignore
+          include-hidden-files: true
 
   coverage:
     name: "Combine & check coverage."
diff --git a/HISTORY.md b/HISTORY.md
index 78e261df..23682343 100644
--- a/HISTORY.md
+++ b/HISTORY.md
@@ -9,6 +9,11 @@ The third number is for emergencies when we need to start branches for older rel
 
 Our backwards-compatibility policy can be found [here](https://github.com/python-attrs/cattrs/blob/main/.github/SECURITY.md).
 
+## 24.1.1 (UNRELEASED)
+
+- Fix {meth}`BaseConverter.register_structure_hook_factory` and {meth}`BaseConverter.register_unstructure_hook_factory` type hints.
+  ([#578](https://github.com/python-attrs/cattrs/issues/578) [#579](https://github.com/python-attrs/cattrs/pull/579))
+
 ## 24.1.0 (2024-08-28)
 
 - **Potentially breaking**: Unstructuring hooks for `typing.Any` are consistent now: values are unstructured using their runtime type.
diff --git a/README.md b/README.md
index acec772e..cb30014e 100644
--- a/README.md
+++ b/README.md
@@ -37,7 +37,6 @@ _cattrs_ works best with [_attrs_](https://www.attrs.org/) classes, and [datacla
 C(a=1, b=['x', 'y'])
 >>> unstructure(instance)
 {'a': 1, 'b': ['x', 'y']}
-
 ```
 
 <!-- end-teaser -->
diff --git a/src/cattrs/converters.py b/src/cattrs/converters.py
index 8d283b30..2759ee7a 100644
--- a/src/cattrs/converters.py
+++ b/src/cattrs/converters.py
@@ -102,17 +102,35 @@
 )
 
 # The Extended factory also takes a converter.
-ExtendedUnstructureHookFactory = TypeVar(
-    "ExtendedUnstructureHookFactory",
-    bound=Callable[[TargetType, "BaseConverter"], UnstructureHook],
+ExtendedUnstructureHookFactory: TypeAlias = Callable[[TargetType, T], UnstructureHook]
+
+# This typevar for the BaseConverter.
+AnyUnstructureHookFactoryBase = TypeVar(
+    "AnyUnstructureHookFactoryBase",
+    bound="HookFactory[UnstructureHook] | ExtendedUnstructureHookFactory[BaseConverter]",
+)
+
+# This typevar for the Converter.
+AnyUnstructureHookFactory = TypeVar(
+    "AnyUnstructureHookFactory",
+    bound="HookFactory[UnstructureHook] | ExtendedUnstructureHookFactory[Converter]",
 )
 
 StructureHookFactory = TypeVar("StructureHookFactory", bound=HookFactory[StructureHook])
 
 # The Extended factory also takes a converter.
-ExtendedStructureHookFactory = TypeVar(
-    "ExtendedStructureHookFactory",
-    bound=Callable[[TargetType, "BaseConverter"], StructureHook],
+ExtendedStructureHookFactory: TypeAlias = Callable[[TargetType, T], StructureHook]
+
+# This typevar for the BaseConverter.
+AnyStructureHookFactoryBase = TypeVar(
+    "AnyStructureHookFactoryBase",
+    bound="HookFactory[StructureHook] | ExtendedStructureHookFactory[BaseConverter]",
+)
+
+# This typevar for the Converter.
+AnyStructureHookFactory = TypeVar(
+    "AnyStructureHookFactory",
+    bound="HookFactory[StructureHook] | ExtendedStructureHookFactory[Converter]",
 )
 
 
@@ -341,12 +359,7 @@ def register_unstructure_hook_func(
     @overload
     def register_unstructure_hook_factory(
         self, predicate: Predicate
-    ) -> Callable[[UnstructureHookFactory], UnstructureHookFactory]: ...
-
-    @overload
-    def register_unstructure_hook_factory(
-        self, predicate: Predicate
-    ) -> Callable[[ExtendedUnstructureHookFactory], ExtendedUnstructureHookFactory]: ...
+    ) -> Callable[[AnyUnstructureHookFactoryBase], AnyUnstructureHookFactoryBase]: ...
 
     @overload
     def register_unstructure_hook_factory(
@@ -355,8 +368,10 @@ def register_unstructure_hook_factory(
 
     @overload
     def register_unstructure_hook_factory(
-        self, predicate: Predicate, factory: ExtendedUnstructureHookFactory
-    ) -> ExtendedUnstructureHookFactory: ...
+        self,
+        predicate: Predicate,
+        factory: ExtendedUnstructureHookFactory[BaseConverter],
+    ) -> ExtendedUnstructureHookFactory[BaseConverter]: ...
 
     def register_unstructure_hook_factory(self, predicate, factory=None):
         """
@@ -478,12 +493,7 @@ def register_structure_hook_func(
     @overload
     def register_structure_hook_factory(
         self, predicate: Predicate
-    ) -> Callable[[StructureHookFactory, StructureHookFactory]]: ...
-
-    @overload
-    def register_structure_hook_factory(
-        self, predicate: Predicate
-    ) -> Callable[[ExtendedStructureHookFactory, ExtendedStructureHookFactory]]: ...
+    ) -> Callable[[AnyStructureHookFactoryBase], AnyStructureHookFactoryBase]: ...
 
     @overload
     def register_structure_hook_factory(
@@ -492,8 +502,8 @@ def register_structure_hook_factory(
 
     @overload
     def register_structure_hook_factory(
-        self, predicate: Predicate, factory: ExtendedStructureHookFactory
-    ) -> ExtendedStructureHookFactory: ...
+        self, predicate: Predicate, factory: ExtendedStructureHookFactory[BaseConverter]
+    ) -> ExtendedStructureHookFactory[BaseConverter]: ...
 
     def register_structure_hook_factory(self, predicate, factory=None):
         """
@@ -1159,6 +1169,44 @@ def __init__(
         self._struct_copy_skip = self._structure_func.get_num_fns()
         self._unstruct_copy_skip = self._unstructure_func.get_num_fns()
 
+    @overload
+    def register_unstructure_hook_factory(
+        self, predicate: Predicate
+    ) -> Callable[[AnyUnstructureHookFactory], AnyUnstructureHookFactory]: ...
+
+    @overload
+    def register_unstructure_hook_factory(
+        self, predicate: Predicate, factory: UnstructureHookFactory
+    ) -> UnstructureHookFactory: ...
+
+    @overload
+    def register_unstructure_hook_factory(
+        self, predicate: Predicate, factory: ExtendedUnstructureHookFactory[Converter]
+    ) -> ExtendedUnstructureHookFactory[Converter]: ...
+
+    def register_unstructure_hook_factory(self, predicate, factory=None):
+        # This dummy wrapper is required due to how `@overload` works.
+        return super().register_unstructure_hook_factory(predicate, factory)
+
+    @overload
+    def register_structure_hook_factory(
+        self, predicate: Predicate
+    ) -> Callable[[AnyStructureHookFactory], AnyStructureHookFactory]: ...
+
+    @overload
+    def register_structure_hook_factory(
+        self, predicate: Predicate, factory: StructureHookFactory
+    ) -> StructureHookFactory: ...
+
+    @overload
+    def register_structure_hook_factory(
+        self, predicate: Predicate, factory: ExtendedStructureHookFactory[Converter]
+    ) -> ExtendedStructureHookFactory[Converter]: ...
+
+    def register_structure_hook_factory(self, predicate, factory=None):
+        # This dummy wrapper is required due to how `@overload` works.
+        return super().register_structure_hook_factory(predicate, factory)
+
     def get_structure_newtype(self, type: type[T]) -> Callable[[Any, Any], T]:
         base = get_newtype_base(type)
         handler = self.get_structure_hook(base)