Index: lib/Sema/AnalysisBasedWarnings.cpp
===================================================================
--- lib/Sema/AnalysisBasedWarnings.cpp
+++ lib/Sema/AnalysisBasedWarnings.cpp
@@ -293,7 +293,7 @@
   if (Throw->getSubExpr())
     ThrowType = Throw->getSubExpr()->getType().getTypePtrOrNull();
   if (!ThrowType)
-    return false;
+    return true;
   const Type *CaughtType = Catch->getCaughtType().getTypePtrOrNull();
   if (!CaughtType)
     return true;
Index: test/SemaCXX/warn-throw-out-noexcept-func.cpp
===================================================================
--- test/SemaCXX/warn-throw-out-noexcept-func.cpp
+++ test/SemaCXX/warn-throw-out-noexcept-func.cpp
@@ -239,12 +239,22 @@
   } catch (const S &s) {
   }
 }
-void o_ShouldDiag() noexcept { //expected-note {{function declared non-throwing here}}
+// As seen in p34973, this should not throw the warning.  If there is an active
+// exception, catch(...) catches everything. 
+void o_ShouldNotDiag() noexcept {
   try {
-    throw; //expected-warning {{has a non-throwing exception specification but}}
+    throw;
   } catch (...) {
   }
 }
+// In fact, a rethrow with ANY catch should be trusted here, otherwise it is
+// going to result in many false positives.
+void p_ShouldNotDiag() noexcept {
+  try {
+    throw;
+  } catch (int){
+  }
+}
 
 #define NOEXCEPT noexcept
 void with_macro() NOEXCEPT { //expected-note {{function declared non-throwing here}}