diff --git a/include/kangaru/detail/cache.hpp b/include/kangaru/detail/cache.hpp
index e578d93..e9f4c3e 100644
--- a/include/kangaru/detail/cache.hpp
+++ b/include/kangaru/detail/cache.hpp
@@ -131,6 +131,14 @@ namespace kangaru {
 			std::ranges::swap(cache, other.cache);
 		}
 		
+		template<forwarded<with_cache> Original, forwarded_source NewSource>
+		static constexpr auto rebind(Original&& original, NewSource&& new_source) -> with_cache<std::decay_t<NewSource>, source_reference_wrapper<unwrapped_cache_type>> {
+			return with_cache<std::decay_t<NewSource>, source_reference_wrapper<unwrapped_cache_type>>{
+				KANGARU5_FWD(new_source),
+				KANGARU5_NO_ADL(ref)(original.cache)
+			};
+		}
+		
 	private:
 		template<typename To>
 		static constexpr auto cast(detail::cache::adl_castable_to<To> auto&& any) -> To {
diff --git a/include/kangaru/detail/heap_storage.hpp b/include/kangaru/detail/heap_storage.hpp
index 778682a..14dc0c6 100644
--- a/include/kangaru/detail/heap_storage.hpp
+++ b/include/kangaru/detail/heap_storage.hpp
@@ -183,6 +183,14 @@ namespace kangaru {
 			return KANGARU5_NO_ADL(maybe_unwrap)(storage).emplace_from(function);
 		}
 		
+		template<forwarded<with_heap_storage> Original, forwarded_source NewSource>
+		static constexpr auto rebind(Original&& original, NewSource&& new_source) -> with_heap_storage<std::decay_t<NewSource>, source_reference_wrapper<maybe_wrapped_t<Storage>>> {
+			return with_heap_storage<std::decay_t<NewSource>, source_reference_wrapper<maybe_wrapped_t<Storage>>>{
+				KANGARU5_FWD(new_source),
+				KANGARU5_NO_ADL(ref)(original.storage)
+			};
+		}
+		
 	private:
 		template<pointer T> requires source_of<source_type, std::remove_pointer_t<T>>
 		friend constexpr auto provide(forwarded<with_heap_storage> auto&& source) -> T {
diff --git a/include/kangaru/detail/recursive_source.hpp b/include/kangaru/detail/recursive_source.hpp
index ff5040e..ce884b6 100644
--- a/include/kangaru/detail/recursive_source.hpp
+++ b/include/kangaru/detail/recursive_source.hpp
@@ -235,6 +235,11 @@ namespace kangaru {
 			}
 		}
 		
+		template<forwarded<with_construction> Original, forwarded_source NewSource>
+		static constexpr auto rebind(Original&& original, NewSource&& new_source) -> with_construction<std::decay_t<NewSource>, Construction> {
+			return with_construction<std::decay_t<NewSource>, Construction>{KANGARU5_FWD(new_source), original.construction};
+		}
+		
 		Source source;
 		
 	private:
diff --git a/include/kangaru/detail/source_helper.hpp b/include/kangaru/detail/source_helper.hpp
index 431841e..2877d46 100644
--- a/include/kangaru/detail/source_helper.hpp
+++ b/include/kangaru/detail/source_helper.hpp
@@ -20,14 +20,6 @@ namespace kangaru {
 			};
 		};
 		
-		template<template<typename, typename> typename Branch, kangaru::source Source, typename State>
-		struct rebind_wrapper<Branch<Source, State>> {
-			template<kangaru::source NewSource, typename NewState = State> requires requires { typename Branch<NewSource, NewState>; }
-			struct ttype {
-				using type = Branch<NewSource, NewState>;
-			};
-		};
-		
 		template<template<typename> typename Branch, kangaru::source Source>
 		struct rebind_wrapper<Branch<Source> const> {
 			template<kangaru::source NewSource> requires requires { typename Branch<NewSource>; }
@@ -35,30 +27,11 @@ namespace kangaru {
 				using type = Branch<NewSource>;
 			};
 		};
-		
-		template<template<typename, typename> typename Branch, kangaru::source Source, typename State>
-		struct rebind_wrapper<Branch<Source, State> const> {
-			template<kangaru::source NewSource, typename NewState = State> requires requires { typename Branch<NewSource, NewState>; }
-			struct ttype {
-				using type = Branch<NewSource, NewState>;
-			};
-		};
 	} // namespace detail::source_helper
 	
 	template<typename Source>
-	concept weak_rebindable_wrapping_source =
+	concept transparent_rebindable_wrapping_source =
 		    wrapping_source<Source>
-		and requires {
-			typename std::type_identity_t<
-				typename detail::source_helper::rebind_wrapper<Source>::template ttype<
-					wrapped_source_t<Source>
-				>::type
-			>;
-		};
-	
-	template<typename Source>
-	concept stateless_rebindable_wrapping_source =
-		    weak_rebindable_wrapping_source<Source>
 		and requires(Source source) {
 			typename std::type_identity_t<
 				typename detail::source_helper::rebind_wrapper<Source>::template ttype<
@@ -69,34 +42,24 @@ namespace kangaru {
 				typename detail::source_helper::rebind_wrapper<Source>::template ttype<std::decay_t<decltype(source.source)>>::type,
 				std::decay_t<decltype(source.source)>
 			>;
-		};;
+		};
 	
 	template<typename Source>
 	concept stateful_rebindable_wrapping_source =
-		    weak_rebindable_wrapping_source<Source>
+		    wrapping_source<Source>
 		and requires(Source source) {
-			typename std::type_identity_t<
-				typename detail::source_helper::rebind_wrapper<Source>::template ttype<
-					std::decay_t<decltype(source.source)>,
-					decltype(KANGARU5_NO_ADL(ref)(source))
-				>::type
-			>;
-			requires std::constructible_from<
-				typename detail::source_helper::rebind_wrapper<Source>::template ttype<
-					std::decay_t<decltype(source.source)>,
-					decltype(KANGARU5_NO_ADL(ref)(source))
-				>::type,
-				std::decay_t<decltype(source.source)>,
-				decltype(KANGARU5_NO_ADL(ref)(source))
-			>;
+			Source::rebind(source, none_source{});
 		};
 	
 	template<typename Source>
 	concept rebindable_wrapping_source =
-		   stateless_rebindable_wrapping_source<Source>
+		   transparent_rebindable_wrapping_source<Source>
 		or stateful_rebindable_wrapping_source<Source>;
 	
 	namespace detail::source_helper {
+		// TODO: Design an interface where rebinding might branch off in composed sources
+		// and allow rebinding with a transformed leaf instead of ignoring it.
+
 		// Forward declaration because otherwise the top overloads cannot find the bottom ones.
 		template<kangaru::source Leaf> requires (not reference_wrapper<Leaf> and not rebindable_wrapping_source<Leaf>)
 		constexpr auto rebind_source_tree(forwarded_source auto&& new_leaf, Leaf&) noexcept;
@@ -124,15 +87,8 @@ namespace kangaru {
 		template<rebindable_wrapping_source Wrapper> requires (not reference_wrapper<Wrapper>)
 		constexpr auto rebind_source_tree(forwarded_source auto&& new_leaf, Wrapper& source) noexcept {
 			if constexpr (stateful_rebindable_wrapping_source<Wrapper>) {
-				using rebound = typename detail::source_helper::rebind_wrapper<Wrapper>::template ttype<
-					decltype(KANGARU5_NO_ADL(rebind_source_tree)(KANGARU5_FWD(new_leaf), source.source)),
-					decltype(KANGARU5_NO_ADL(ref)(source))
-				>::type;
-				return rebound{
-					KANGARU5_NO_ADL(rebind_source_tree)(KANGARU5_FWD(new_leaf), source.source),
-					KANGARU5_NO_ADL(ref)(source),
-				};
-			} else if constexpr (stateless_rebindable_wrapping_source<Wrapper>) {
+				return Wrapper::rebind(source, KANGARU5_NO_ADL(rebind_source_tree)(KANGARU5_FWD(new_leaf), source.source));
+			} else if constexpr (transparent_rebindable_wrapping_source<Wrapper>) {
 				using rebound = typename detail::source_helper::rebind_wrapper<Wrapper>::template ttype<
 					decltype(KANGARU5_NO_ADL(rebind_source_tree)(KANGARU5_FWD(new_leaf), source.source))
 				>::type;
@@ -143,16 +99,6 @@ namespace kangaru {
 				static_assert(not std::same_as<Wrapper, Wrapper>, "exhaustive");
 			}
 		}
-		
-		template<typename Source> requires (forwarded_source<Source> and not wrapping_source<std::remove_reference_t<Source>>)
-		constexpr auto source_tree_leaf(Source&& source) -> auto&& {
-			return KANGARU5_FWD(source);
-		}
-		
-		template<typename Source> requires (wrapping_source<std::remove_reference_t<Source>>)
-		constexpr auto source_tree_leaf(Source&& source) -> auto&& {
-			return KANGARU5_NO_ADL(source_tree_leaf)(KANGARU5_FWD(source).source);
-		}
 	} // namespace detail::source_helper
 } // namespace kangaru
 
diff --git a/include/kangaru/detail/source_types.hpp b/include/kangaru/detail/source_types.hpp
index cde9976..6f03adc 100644
--- a/include/kangaru/detail/source_types.hpp
+++ b/include/kangaru/detail/source_types.hpp
@@ -250,6 +250,14 @@ namespace kangaru {
 			return kangaru::provide<T>(KANGARU5_FWD(source).source);
 		}
 		
+		template<forwarded<with_alternative> Original, forwarded_source NewSource>
+		static constexpr auto rebind(Original&& original, NewSource&& new_source) -> with_alternative<std::decay_t<NewSource>, source_reference_wrapper<maybe_wrapped_t<Alternative>>> {
+			return with_alternative<std::decay_t<NewSource>, source_reference_wrapper<maybe_wrapped_t<Alternative>>>{
+				KANGARU5_FWD(new_source),
+				KANGARU5_NO_ADL(ref)(original.alternative)
+			};
+		}
+		
 	private:
 		Alternative alternative;
 	};