diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
index a6c256f32dfa..4ae1c6d5bfbd 100644
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -4955,11 +4955,18 @@ OverflowResult llvm::computeOverflowForUnsignedSub(const Value *LHS,
   // X - (X % ?)
   // The remainder of a value can't have greater magnitude than itself,
   // so the subtraction can't overflow.
+
+  // X - (X -nuw ?)
+  // In the minimal case, this would simplify to "?", so there's no subtract
+  // at all. But if this analysis is used to peek through casts, for example,
+  // then determining no-overflow may allow other transforms.
+
   // TODO: There are other patterns like this.
   //       See simplifyICmpWithBinOpOnLHS() for candidates.
-  if (match(RHS, m_URem(m_Specific(LHS), m_Value())) &&
-      isGuaranteedNotToBeUndefOrPoison(LHS, AC, CxtI, DT))
-    return OverflowResult::NeverOverflows;
+  if (match(RHS, m_URem(m_Specific(LHS), m_Value())) ||
+      match(RHS, m_NUWSub(m_Specific(LHS), m_Value())))
+    if (isGuaranteedNotToBeUndefOrPoison(LHS, AC, CxtI, DT))
+      return OverflowResult::NeverOverflows;
 
   // Checking for conditions implied by dominating conditions may be expensive.
   // Limit it to usub_with_overflow calls for now.
diff --git a/llvm/test/Transforms/InstCombine/sub.ll b/llvm/test/Transforms/InstCombine/sub.ll
index 039441f9188a..f7d99a084176 100644
--- a/llvm/test/Transforms/InstCombine/sub.ll
+++ b/llvm/test/Transforms/InstCombine/sub.ll
@@ -1926,10 +1926,7 @@ define i16 @srem_sext_noundef(i8 noundef %x, i8 %y) {
 
 define i16 @zext_nuw_noundef(i8 noundef %x, i8 %y) {
 ; CHECK-LABEL: @zext_nuw_noundef(
-; CHECK-NEXT:    [[D:%.*]] = sub nuw i8 [[X:%.*]], [[Y:%.*]]
-; CHECK-NEXT:    [[EX:%.*]] = zext i8 [[X]] to i16
-; CHECK-NEXT:    [[ED:%.*]] = zext i8 [[D]] to i16
-; CHECK-NEXT:    [[Z:%.*]] = sub nsw i16 [[EX]], [[ED]]
+; CHECK-NEXT:    [[Z:%.*]] = zext i8 [[Y:%.*]] to i16
 ; CHECK-NEXT:    ret i16 [[Z]]
 ;
   %d = sub nuw i8 %x, %y
@@ -1939,6 +1936,8 @@ define i16 @zext_nuw_noundef(i8 noundef %x, i8 %y) {
   ret i16 %z
 }
 
+; negative test - requires noundef
+
 define i16 @zext_nuw(i8 %x, i8 %y) {
 ; CHECK-LABEL: @zext_nuw(
 ; CHECK-NEXT:    [[D:%.*]] = sub nuw i8 [[X:%.*]], [[Y:%.*]]
@@ -1954,6 +1953,8 @@ define i16 @zext_nuw(i8 %x, i8 %y) {
   ret i16 %z
 }
 
+; negative test - requires nuw
+
 define i16 @zext_noundef(i8 noundef %x, i8 %y) {
 ; CHECK-LABEL: @zext_noundef(
 ; CHECK-NEXT:    [[D:%.*]] = sub i8 [[X:%.*]], [[Y:%.*]]
@@ -1969,6 +1970,8 @@ define i16 @zext_noundef(i8 noundef %x, i8 %y) {
   ret i16 %z
 }
 
+; negative test - must have common operand
+
 define i16 @zext_nsw_noundef_wrong_val(i8 noundef %x, i8 noundef %y, i8 noundef %q) {
 ; CHECK-LABEL: @zext_nsw_noundef_wrong_val(
 ; CHECK-NEXT:    [[D:%.*]] = sub nuw i8 [[X:%.*]], [[Y:%.*]]
@@ -1984,13 +1987,12 @@ define i16 @zext_nsw_noundef_wrong_val(i8 noundef %x, i8 noundef %y, i8 noundef
   ret i16 %z
 }
 
-define i16 @srem_zext_noundef(i8 noundef %x, i8 %y) {
-; CHECK-LABEL: @srem_zext_noundef(
+; two no-wrap analyses combine to allow reduction
+
+define i16 @urem_zext_noundef(i8 noundef %x, i8 %y) {
+; CHECK-LABEL: @urem_zext_noundef(
 ; CHECK-NEXT:    [[R:%.*]] = urem i8 [[X:%.*]], [[Y:%.*]]
-; CHECK-NEXT:    [[D:%.*]] = sub nuw i8 [[X]], [[R]]
-; CHECK-NEXT:    [[ED:%.*]] = zext i8 [[D]] to i16
-; CHECK-NEXT:    [[EX:%.*]] = zext i8 [[X]] to i16
-; CHECK-NEXT:    [[Z:%.*]] = sub nsw i16 [[EX]], [[ED]]
+; CHECK-NEXT:    [[Z:%.*]] = zext i8 [[R]] to i16
 ; CHECK-NEXT:    ret i16 [[Z]]
 ;
   %r = urem i8 %x, %y