diff --git a/llvm/lib/Analysis/InstructionSimplify.cpp b/llvm/lib/Analysis/InstructionSimplify.cpp
--- a/llvm/lib/Analysis/InstructionSimplify.cpp
+++ b/llvm/lib/Analysis/InstructionSimplify.cpp
@@ -4118,6 +4118,17 @@
   if (TrueVal == FalseVal)
     return TrueVal;
 
+  // If the true or false value is undef, we can fold to the other value as
+  // long as the other value isn't poison.
+  // select ?, undef, X -> X
+  if (isa<UndefValue>(TrueVal) &&
+      isGuaranteedNotToBeUndefOrPoison(FalseVal, Q.CxtI, Q.DT))
+    return FalseVal;
+  // select ?, X, undef -> X
+  if (isa<UndefValue>(FalseVal) &&
+      isGuaranteedNotToBeUndefOrPoison(TrueVal, Q.CxtI, Q.DT))
+    return TrueVal;
+
   // Deal with partial undef vector constants: select ?, VecC, VecC' --> VecC''
   Constant *TrueC, *FalseC;
   if (TrueVal->getType()->isVectorTy() && match(TrueVal, m_Constant(TrueC)) &&
diff --git a/llvm/test/Transforms/InstSimplify/select.ll b/llvm/test/Transforms/InstSimplify/select.ll
--- a/llvm/test/Transforms/InstSimplify/select.ll
+++ b/llvm/test/Transforms/InstSimplify/select.ll
@@ -794,8 +794,7 @@
 ; These can be folded because the other value is guaranteed not to be poison.
 define i32 @false_undef_true_constant(i1 %cond) {
 ; CHECK-LABEL: @false_undef_true_constant(
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[COND:%.*]], i32 10, i32 undef
-; CHECK-NEXT:    ret i32 [[S]]
+; CHECK-NEXT:    ret i32 10
 ;
   %s = select i1 %cond, i32 10, i32 undef
   ret i32 %s
@@ -803,8 +802,7 @@
 
 define i32 @true_undef_false_constant(i1 %cond) {
 ; CHECK-LABEL: @true_undef_false_constant(
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[COND:%.*]], i32 undef, i32 20
-; CHECK-NEXT:    ret i32 [[S]]
+; CHECK-NEXT:    ret i32 20
 ;
   %s = select i1 %cond, i32 undef, i32 20
   ret i32 %s
@@ -830,8 +828,7 @@
 define i32 @false_undef_true_freeze(i1 %cond, i32 %x) {
 ; CHECK-LABEL: @false_undef_true_freeze(
 ; CHECK-NEXT:    [[XF:%.*]] = freeze i32 [[X:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[COND:%.*]], i32 [[XF]], i32 undef
-; CHECK-NEXT:    ret i32 [[S]]
+; CHECK-NEXT:    ret i32 [[XF]]
 ;
   %xf = freeze i32 %x
   %s = select i1 %cond, i32 %xf, i32 undef
@@ -841,8 +838,7 @@
 define i32 @false_undef_false_freeze(i1 %cond, i32 %x) {
 ; CHECK-LABEL: @false_undef_false_freeze(
 ; CHECK-NEXT:    [[XF:%.*]] = freeze i32 [[X:%.*]]
-; CHECK-NEXT:    [[S:%.*]] = select i1 [[COND:%.*]], i32 undef, i32 [[XF]]
-; CHECK-NEXT:    ret i32 [[S]]
+; CHECK-NEXT:    ret i32 [[XF]]
 ;
   %xf = freeze i32 %x
   %s = select i1 %cond, i32 undef, i32 %xf