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
@@ -1382,6 +1382,27 @@
 
   ICmpInst::Predicate UnsignedPred;
 
+  Value *ComparedWith;
+  if (match(UnsignedICmp,
+            m_c_ICmp(UnsignedPred, m_Specific(Y), m_Value(ComparedWith))) &&
+      match(Y, m_c_Add(m_Specific(ComparedWith), m_Value()))) {
+    if (UnsignedICmp->getOperand(0) != Y)
+      UnsignedPred = ICmpInst::getSwappedPredicate(UnsignedPred);
+
+    // Given  Y = (A + B)
+    //   Y >= ComparedWith && Y == 0  --> false
+    //   Y <  ComparedWith || Y != 0  --> true
+    // iff ComparedWith is A or B and is non-zero.
+    if (UnsignedPred == ICmpInst::ICMP_UGE && EqPred == ICmpInst::ICMP_EQ &&
+        IsAnd &&
+        isKnownNonZero(ComparedWith, Q.DL, /*Depth=*/0, Q.AC, Q.CxtI, Q.DT))
+      return ConstantInt::getFalse(UnsignedICmp->getType());
+    if (UnsignedPred == ICmpInst::ICMP_ULT && EqPred == ICmpInst::ICMP_NE &&
+        !IsAnd &&
+        isKnownNonZero(ComparedWith, Q.DL, /*Depth=*/0, Q.AC, Q.CxtI, Q.DT))
+      return ConstantInt::getTrue(UnsignedICmp->getType());
+  }
+
   Value *A, *B;
   // Y = (A - B);
   if (match(Y, m_Sub(m_Value(A), m_Value(B)))) {
diff --git a/llvm/test/Transforms/InstSimplify/result-of-add-of-negative-is-non-zero-and-no-underflow.ll b/llvm/test/Transforms/InstSimplify/result-of-add-of-negative-is-non-zero-and-no-underflow.ll
--- a/llvm/test/Transforms/InstSimplify/result-of-add-of-negative-is-non-zero-and-no-underflow.ll
+++ b/llvm/test/Transforms/InstSimplify/result-of-add-of-negative-is-non-zero-and-no-underflow.ll
@@ -18,10 +18,7 @@
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[CMP]])
 ; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i8 [[BASE]], [[OFFSET:%.*]]
 ; CHECK-NEXT:    call void @use8(i8 [[ADJUSTED]])
-; CHECK-NEXT:    [[NOT_NULL:%.*]] = icmp ne i8 [[ADJUSTED]], 0
-; CHECK-NEXT:    [[NO_UNDERFLOW:%.*]] = icmp ult i8 [[ADJUSTED]], [[BASE]]
-; CHECK-NEXT:    [[R:%.*]] = or i1 [[NOT_NULL]], [[NO_UNDERFLOW]]
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 true
 ;
   %cmp = icmp slt i8 %base, 0
   call void @llvm.assume(i1 %cmp)
@@ -39,10 +36,7 @@
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[CMP]])
 ; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i8 [[BASE]], [[OFFSET:%.*]]
 ; CHECK-NEXT:    call void @use8(i8 [[ADJUSTED]])
-; CHECK-NEXT:    [[NOT_NULL:%.*]] = icmp ne i8 [[ADJUSTED]], 0
-; CHECK-NEXT:    [[NO_UNDERFLOW:%.*]] = icmp ugt i8 [[BASE]], [[ADJUSTED]]
-; CHECK-NEXT:    [[R:%.*]] = or i1 [[NOT_NULL]], [[NO_UNDERFLOW]]
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 true
 ;
   %cmp = icmp slt i8 %base, 0
   call void @llvm.assume(i1 %cmp)
@@ -63,10 +57,7 @@
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[CMP]])
 ; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i8 [[BASE]], [[OFFSET:%.*]]
 ; CHECK-NEXT:    call void @use8(i8 [[ADJUSTED]])
-; CHECK-NEXT:    [[NOT_NULL:%.*]] = icmp eq i8 [[ADJUSTED]], 0
-; CHECK-NEXT:    [[NO_UNDERFLOW:%.*]] = icmp uge i8 [[ADJUSTED]], [[BASE]]
-; CHECK-NEXT:    [[R:%.*]] = and i1 [[NOT_NULL]], [[NO_UNDERFLOW]]
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %cmp = icmp slt i8 %base, 0
   call void @llvm.assume(i1 %cmp)
@@ -84,10 +75,7 @@
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[CMP]])
 ; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i8 [[BASE]], [[OFFSET:%.*]]
 ; CHECK-NEXT:    call void @use8(i8 [[ADJUSTED]])
-; CHECK-NEXT:    [[NOT_NULL:%.*]] = icmp eq i8 [[ADJUSTED]], 0
-; CHECK-NEXT:    [[NO_UNDERFLOW:%.*]] = icmp ule i8 [[BASE]], [[ADJUSTED]]
-; CHECK-NEXT:    [[R:%.*]] = and i1 [[NOT_NULL]], [[NO_UNDERFLOW]]
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %cmp = icmp slt i8 %base, 0
   call void @llvm.assume(i1 %cmp)
@@ -99,3 +87,27 @@
   %r = and i1 %not_null, %no_underflow
   ret i1 %r
 }
+
+; We need to know that the value we compare with here (%base) is non-zero,
+; so knowledge about %offset won't do.
+define i1 @t5_bad(i8 %base, i8 %offset) {
+; CHECK-LABEL: @t5_bad(
+; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i8 [[OFFSET:%.*]], 0
+; CHECK-NEXT:    call void @llvm.assume(i1 [[CMP]])
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i8 [[BASE:%.*]], [[OFFSET]]
+; CHECK-NEXT:    call void @use8(i8 [[ADJUSTED]])
+; CHECK-NEXT:    [[NOT_NULL:%.*]] = icmp ne i8 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_UNDERFLOW:%.*]] = icmp ult i8 [[ADJUSTED]], [[BASE]]
+; CHECK-NEXT:    [[R:%.*]] = or i1 [[NOT_NULL]], [[NO_UNDERFLOW]]
+; CHECK-NEXT:    ret i1 [[R]]
+;
+  %cmp = icmp slt i8 %offset, 0
+  call void @llvm.assume(i1 %cmp)
+
+  %adjusted = add i8 %base, %offset
+  call void @use8(i8 %adjusted)
+  %not_null = icmp ne i8 %adjusted, 0
+  %no_underflow = icmp ult i8 %adjusted, %base
+  %r = or i1 %not_null, %no_underflow
+  ret i1 %r
+}