Index: clang/lib/Sema/SemaTemplateDeduction.cpp
===================================================================
--- clang/lib/Sema/SemaTemplateDeduction.cpp
+++ clang/lib/Sema/SemaTemplateDeduction.cpp
@@ -2851,11 +2851,6 @@
     VarTemplatePartialSpecializationDecl *Spec) {
   return !Spec->isClassScopeExplicitSpecialization();
 }
-template <>
-bool DeducedArgsNeedReplacement<ClassTemplatePartialSpecializationDecl>(
-    ClassTemplatePartialSpecializationDecl *Spec) {
-  return !Spec->isClassScopeExplicitSpecialization();
-}
 
 template <typename TemplateDeclT>
 static Sema::TemplateDeductionResult
Index: clang/lib/Sema/SemaTemplateInstantiate.cpp
===================================================================
--- clang/lib/Sema/SemaTemplateInstantiate.cpp
+++ clang/lib/Sema/SemaTemplateInstantiate.cpp
@@ -310,6 +310,16 @@
     if (const auto *VarTemplSpec =
             dyn_cast<VarTemplateSpecializationDecl>(CurDecl)) {
       R = HandleVarTemplateSpec(VarTemplSpec, Result, SkipForSpecialization);
+    } else if (const auto *PartialClassTemplSpec =
+                   dyn_cast<ClassTemplatePartialSpecializationDecl>(CurDecl)) {
+      // We don't want the arguments from the Partial Specialization, since
+      // anything instantiating here cannot access the arguments from the
+      // specialized template anyway, so any substitution we would do with these
+      // partially specialized arguments would 'wrong' and confuse constraint
+      // instantiation. We only do this in the case of a constraint check, since
+      // code elsewhere actually uses these and replaces them later with what
+      // they mean.
+      R = Response::UseNextDecl(PartialClassTemplSpec);
     } else if (const auto *ClassTemplSpec =
                    dyn_cast<ClassTemplateSpecializationDecl>(CurDecl)) {
       R = HandleClassTemplateSpec(ClassTemplSpec, Result,
Index: clang/test/SemaTemplate/concepts.cpp
===================================================================
--- clang/test/SemaTemplate/concepts.cpp
+++ clang/test/SemaTemplate/concepts.cpp
@@ -825,3 +825,34 @@
   template<C<int> U> friend constexpr auto decltype(L<int>)::operator()() const;
 };
 } // namespace TemplateInsideNonTemplateClass
+
+namespace GH61959 {
+template <typename T0>
+concept C = (sizeof(T0) >= 4);
+
+template<typename...>
+struct Orig { };
+
+template<typename T>
+struct Orig<T> {
+  template<typename> requires C<T>
+  void f() { }
+
+  template<typename> requires true
+  void f() { }
+};
+
+template <typename...> struct Mod {};
+
+template <typename T1, typename T2>
+struct Mod<T1, T2> {
+  template <typename> requires C<T1>
+  constexpr static int f() { return 1; }
+
+  template <typename> requires C<T2>
+  constexpr static int f() { return 2; }
+};
+
+static_assert(Mod<int, char>::f<double>() == 1);
+static_assert(Mod<char, int>::f<double>() == 2);
+}