diff --git a/lib/Analysis/InstructionSimplify.cpp b/lib/Analysis/InstructionSimplify.cpp
index 9d78f8bf404..8709f6bf9d2 100644
--- a/lib/Analysis/InstructionSimplify.cpp
+++ b/lib/Analysis/InstructionSimplify.cpp
@@ -2204,15 +2204,15 @@ Value *llvm::SimplifySelectInst(Value *CondVal, Value *TrueVal, Value *FalseVal,
   if (TrueVal == FalseVal)
     return TrueVal;
 
-  if (isa<UndefValue>(TrueVal))   // select C, undef, X -> X
-    return FalseVal;
-  if (isa<UndefValue>(FalseVal))   // select C, X, undef -> X
-    return TrueVal;
   if (isa<UndefValue>(CondVal)) {  // select undef, X, Y -> X or Y
     if (isa<Constant>(TrueVal))
       return TrueVal;
     return FalseVal;
   }
+  if (isa<UndefValue>(TrueVal))   // select C, undef, X -> X
+    return FalseVal;
+  if (isa<UndefValue>(FalseVal))   // select C, X, undef -> X
+    return TrueVal;
 
   return 0;
 }
diff --git a/lib/VMCore/ConstantFold.cpp b/lib/VMCore/ConstantFold.cpp
index 8cca06fdda0..b7a1350ff5a 100644
--- a/lib/VMCore/ConstantFold.cpp
+++ b/lib/VMCore/ConstantFold.cpp
@@ -730,9 +730,12 @@ Constant *llvm::ConstantFoldSelectInstruction(Constant *Cond,
   }
 
 
+  if (isa<UndefValue>(Cond)) {
+    if (isa<UndefValue>(V1)) return V1;
+    return V2;
+  }
   if (isa<UndefValue>(V1)) return V2;
   if (isa<UndefValue>(V2)) return V1;
-  if (isa<UndefValue>(Cond)) return V1;
   if (V1 == V2) return V1;
 
   if (ConstantExpr *TrueVal = dyn_cast<ConstantExpr>(V1)) {
@@ -1851,7 +1854,9 @@ Constant *llvm::ConstantFoldCompareInstruction(unsigned short pred,
   if (isa<UndefValue>(C1) || isa<UndefValue>(C2)) {
     // For EQ and NE, we can always pick a value for the undef to make the
     // predicate pass or fail, so we can return undef.
-    if (ICmpInst::isEquality(ICmpInst::Predicate(pred)))
+    // Also, if both operands are undef, we can return undef.
+    if (ICmpInst::isEquality(ICmpInst::Predicate(pred)) ||
+        (isa<UndefValue>(C1) && isa<UndefValue>(C2)))
       return UndefValue::get(ResultTy);
     // Otherwise, pick the same value as the non-undef operand, and fold
     // it to true or false.
diff --git a/test/Transforms/InstSimplify/binop.ll b/test/Transforms/InstSimplify/undef.ll
similarity index 75%
rename from test/Transforms/InstSimplify/binop.ll
rename to test/Transforms/InstSimplify/undef.ll
index f4bc55753a5..8134cc84874 100644
--- a/test/Transforms/InstSimplify/binop.ll
+++ b/test/Transforms/InstSimplify/undef.ll
@@ -97,3 +97,31 @@ define i64 @test13() {
   %r = lshr i64 undef, undef
   ret i64 %r
 }
+
+; @test14
+; CHECK: ret i1 undef
+define i1 @test14() {
+  %r = icmp slt i64 undef, undef
+  ret i1 %r
+}
+
+; @test15
+; CHECK: ret i1 undef
+define i1 @test15() {
+  %r = icmp ult i64 undef, undef
+  ret i1 %r
+}
+
+; @test16
+; CHECK: ret i64 undef
+define i64 @test16(i64 %a) {
+  %r = select i1 undef, i64 %a, i64 undef
+  ret i64 %r
+}
+
+; @test17
+; CHECK: ret i64 undef
+define i64 @test17(i64 %a) {
+  %r = select i1 undef, i64 undef, i64 %a
+  ret i64 %r
+}