Index: lib/Analysis/CFLAliasAnalysis.cpp
===================================================================
--- lib/Analysis/CFLAliasAnalysis.cpp
+++ lib/Analysis/CFLAliasAnalysis.cpp
@@ -398,6 +398,8 @@
   }
 
   template <typename InstT> void visitCallLikeInst(InstT &Inst) {
+    // TODO: Add support for noalias args/all the other fun function attributes
+    // that we can tack on.
     SmallVector<Function *, 4> Targets;
     if (getPossibleTargets(&Inst, Targets)) {
       if (tryInterproceduralAnalysis(Targets, &Inst, Inst.arg_operands()))
@@ -406,8 +408,12 @@
       Output.clear();
     }
 
+    // Because the function is opaque, we need to note that anything
+    // could have happened to the arguments, and that the result could alias
+    // just about anything, too.
     for (Value *V : Inst.arg_operands())
       Output.push_back(Edge(&Inst, V, EdgeType::Assign, AttrAll));
+    Output.push_back(Edge(&Inst, &Inst, EdgeType::Assign, AttrAll));
   }
 
   void visitCallInst(CallInst &Inst) { visitCallLikeInst(Inst); }
Index: test/Analysis/CFLAliasAnalysis/opaque-call-alias.ll
===================================================================
--- test/Analysis/CFLAliasAnalysis/opaque-call-alias.ll
+++ test/Analysis/CFLAliasAnalysis/opaque-call-alias.ll
@@ -0,0 +1,20 @@
+; We previously had a case where we would put results from a no-args call in
+; its own stratified set. This would make cases like the one in @test say that
+; nothing (except %Escapes and %Arg) can alias
+
+; RUN: opt < %s -cfl-aa -aa-eval -print-may-aliases -disable-output 2>&1 | FileCheck %s
+
+; CHECK:     Function: test
+; CHECK:     MayAlias: i8* %Arg, i8* %Escapes
+; CHECK:     MayAlias: i8* %Arg, i8* %Retrieved
+; CHECK:     MayAlias: i8* %Escapes, i8* %Retrieved
+define void @test(i8* %Arg) {
+  %Noalias = alloca i8
+  %Escapes = alloca i8
+  call void @set_thepointer(i8* %Escapes)
+  %Retrieved = call i8* @get_thepointer()
+  ret void
+}
+
+declare void @set_thepointer(i8* %P)
+declare i8* @get_thepointer()