Index: lib/Sema/SemaTemplate.cpp
===================================================================
--- lib/Sema/SemaTemplate.cpp
+++ lib/Sema/SemaTemplate.cpp
@@ -8956,6 +8956,7 @@
   //  instantiated from the member definition associated with its class
   //  template.
   UnresolvedSet<8> Matches;
+  FunctionDecl *NonTemplateMatch = nullptr;
   AttributeList *Attr = D.getDeclSpec().getAttributes().getList();
   TemplateSpecCandidateSet FailedCandidates(D.getIdentifierLoc());
   for (LookupResult::iterator P = Previous.begin(), PEnd = Previous.end();
@@ -8966,12 +8967,22 @@
         QualType Adjusted = adjustCCAndNoReturn(R, Method->getType(),
                                                 /*AdjustExceptionSpec*/true);
         if (Context.hasSameUnqualifiedType(Method->getType(), Adjusted)) {
-          Matches.clear();
-
+          if (!Method->getPrimaryTemplate()) {
+            // FIXME: Can this assert ever happen?  Needs a test.
+            assert(!NonTemplateMatch && "Multiple NonTemplateMatches");
+            NonTemplateMatch = Method;
+            continue;
+          }
           Matches.addDecl(Method, P.getAccess());
+
+          // FIXME: Can this ever be true?  Even so, should it really be a
+          // break?  Needs a test.
           if (Method->getTemplateSpecializationKind() == TSK_Undeclared)
             break;
+          continue;
         }
+        // FIXME:  Would this be considered an almost match as well?
+        continue;
       }
     }
 
@@ -9012,19 +9023,22 @@
     Matches.addDecl(Specialization, P.getAccess());
   }
 
-  // Find the most specialized function template specialization.
-  UnresolvedSetIterator Result = getMostSpecialized(
-      Matches.begin(), Matches.end(), FailedCandidates,
-      D.getIdentifierLoc(),
-      PDiag(diag::err_explicit_instantiation_not_known) << Name,
-      PDiag(diag::err_explicit_instantiation_ambiguous) << Name,
-      PDiag(diag::note_explicit_instantiation_candidate));
-
-  if (Result == Matches.end())
-    return true;
+  FunctionDecl *Specialization = NonTemplateMatch;
+  if (!Specialization) {
+    // Find the most specialized function template specialization.
+    UnresolvedSetIterator Result = getMostSpecialized(
+        Matches.begin(), Matches.end(), FailedCandidates,
+        D.getIdentifierLoc(),
+        PDiag(diag::err_explicit_instantiation_not_known) << Name,
+        PDiag(diag::err_explicit_instantiation_ambiguous) << Name,
+        PDiag(diag::note_explicit_instantiation_candidate));
+
+    if (Result == Matches.end())
+      return true;
 
-  // Ignore access control bits, we don't need them for redeclaration checking.
-  FunctionDecl *Specialization = cast<FunctionDecl>(*Result);
+    // Ignore access control bits, we don't need them for redeclaration checking.
+    Specialization = cast<FunctionDecl>(*Result);
+  }
 
   // C++11 [except.spec]p4
   // In an explicit instantiation an exception-specification may be specified,
Index: test/CXX/temp/temp.decls/temp.mem/p5.cpp
===================================================================
--- test/CXX/temp/temp.decls/temp.mem/p5.cpp
+++ test/CXX/temp/temp.decls/temp.mem/p5.cpp
@@ -77,3 +77,16 @@
   x0.operator float *();
   x0c.operator const char*();
 }
+
+namespace PR14211 {
+template <class U> struct X {
+  void foo(U){}
+  template <class T> void foo(T){}
+
+  template <class T> void bar(T){}
+  void bar(U){}
+};
+
+template void X<int>::foo(int);
+template void X<int>::bar(int);
+}