diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -4693,8 +4693,9 @@
     if (isa<UndefValue>(C) || isa<ConstantExpr>(C))
       return false;
 
-    // TODO: Add ConstantFP and pointers.
-    if (isa<ConstantInt>(C) || isa<GlobalVariable>(C) )
+    // TODO: Add ConstantFP.
+    if (isa<ConstantInt>(C) || isa<GlobalVariable>(C) ||
+        isa<ConstantPointerNull>(C))
       return true;
 
     if (C->getType()->isVectorTy())
diff --git a/llvm/test/Transforms/InstSimplify/freeze.ll b/llvm/test/Transforms/InstSimplify/freeze.ll
--- a/llvm/test/Transforms/InstSimplify/freeze.ll
+++ b/llvm/test/Transforms/InstSimplify/freeze.ll
@@ -51,12 +51,9 @@
   ret i32()* %k
 }
 
-; TODO: This is not poison.
-
 define i32* @make_const_null() {
 ; CHECK-LABEL: @make_const_null(
-; CHECK-NEXT:    [[K:%.*]] = freeze i32* null
-; CHECK-NEXT:    ret i32* [[K]]
+; CHECK-NEXT:    ret i32* null
 ;
   %k = freeze i32* null
   ret i32* %k
@@ -208,8 +205,7 @@
 
 define i32* @gep_inbounds_null() {
 ; CHECK-LABEL: @gep_inbounds_null(
-; CHECK-NEXT:    [[K:%.*]] = freeze i32* null
-; CHECK-NEXT:    ret i32* [[K]]
+; CHECK-NEXT:    ret i32* null
 ;
   %p = getelementptr inbounds i32, i32* null, i32 0
   %k = freeze i32* %p