Index: lib/Analysis/LazyValueInfo.cpp
===================================================================
--- lib/Analysis/LazyValueInfo.cpp
+++ lib/Analysis/LazyValueInfo.cpp
@@ -222,12 +222,22 @@
       if (RHS.isConstant()) {
         if (Val == RHS.Val)
           return false;
+
+        PointerType *PT = dyn_cast<PointerType>(Val->getType());
+        if (PT && isKnownNonNull(Val) && isKnownNonNull(RHS.Val))
+          return markNotConstant(ConstantPointerNull::get(PT));
+        
         return markOverdefined();
       }
 
       if (RHS.isNotConstant()) {
         if (Val == RHS.Val)
           return markOverdefined();
+
+        PointerType *PT = dyn_cast<PointerType>(Val->getType());
+        if (PT && isa<ConstantPointerNull>(RHS.Val) && isKnownNonNull(Val))
+          return markNotConstant(ConstantPointerNull::get(PT));
+        
         return markOverdefined();
       }
 
@@ -238,6 +248,11 @@
       if (RHS.isConstant()) {
         if (Val == RHS.Val)
           return markOverdefined();
+
+        PointerType *PT = dyn_cast<PointerType>(Val->getType());
+        if (PT && isa<ConstantPointerNull>(Val) && isKnownNonNull(RHS.Val))
+          return false;
+        
         return markOverdefined();
       }
 
Index: test/Transforms/CorrelatedValuePropagation/select.ll
===================================================================
--- test/Transforms/CorrelatedValuePropagation/select.ll
+++ test/Transforms/CorrelatedValuePropagation/select.ll
@@ -216,3 +216,53 @@
 ; CHECK: ret i1 true
   ret i1 true
 }
+
+define i1 @test7(i1 %unknown, i32* nonnull %p1, i32* nonnull %p2 ) {
+; CHECK-LABEL: @test7
+  %sel = select i1 %unknown, i32* %p1, i32* %p2
+  ;; TODO: This pointless branch shouldn't be neccessary
+  br label %next2
+next2:
+; CHECK-LABEL: next2:
+; CHECK: ret i1 true
+  %res = icmp ne i32* %sel, null
+  ret i1 %res
+}
+@g1 = external global i32
+@g2 = external global i32
+
+define i1 @test8a(i1 %unknown, i32* nonnull %p1) {
+; CHECK-LABEL: @test8
+  %sel = select i1 %unknown, i32* %p1, i32* @g1
+  ;; TODO: This pointless branch shouldn't be neccessary
+  br label %next2
+next2:
+; CHECK-LABEL: next2:
+; CHECK: ret i1 true
+  %res = icmp ne i32* %sel, null
+  ret i1 %res
+}
+
+define i1 @test8b(i1 %unknown, i32* nonnull %p1) {
+; CHECK-LABEL: @test8
+  %sel = select i1 %unknown, i32* %p1, i32* @g1
+  ;; TODO: This pointless branch shouldn't be neccessary
+  br label %next2
+next2:
+; CHECK-LABEL: next2:
+; CHECK: ret i1 true
+  %res = icmp ne i32* %sel, null
+  ret i1 %res
+}
+
+define i1 @test9(i1 %unknown) {
+; CHECK-LABEL: @test9
+  %sel = select i1 %unknown, i32* @g1, i32* @g2
+  ;; TODO: This pointless branch shouldn't be neccessary
+  br label %next2
+next2:
+; CHECK-LABEL: next2:
+; CHECK: ret i1 true
+  %res = icmp ne i32* %sel, null
+  ret i1 %res
+}