diff --git a/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp b/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
@@ -1064,6 +1064,27 @@
 
     break;
   }
+  case Instruction::Add: {
+    unsigned NLZ = DemandedMask.countLeadingZeros();
+    APInt DemandedFromOps = APInt::getLowBitsSet(BitWidth, BitWidth - NLZ);
+
+    // If an operand adds zeros to every bit below the highest demanded bit,
+    // that operand doesn't change the result. Return the other side.
+    computeKnownBits(I->getOperand(1), RHSKnown, Depth + 1, CxtI);
+    if (DemandedFromOps.isSubsetOf(RHSKnown.Zero))
+      return I->getOperand(0);
+
+    computeKnownBits(I->getOperand(0), LHSKnown, Depth + 1, CxtI);
+    if (DemandedFromOps.isSubsetOf(LHSKnown.Zero))
+      return I->getOperand(1);
+
+    bool NSW = cast<OverflowingBinaryOperator>(I)->hasNoSignedWrap();
+    Known = KnownBits::computeForAddSub(true, NSW, LHSKnown, RHSKnown);
+    if (DemandedMask.isSubsetOf(Known.Zero|Known.One))
+      return Constant::getIntegerValue(ITy, Known.One);
+
+    break;
+  }
   case Instruction::AShr: {
     // Compute the Known bits to simplify things downstream.
     computeKnownBits(I, Known, Depth, CxtI);
diff --git a/llvm/test/Transforms/InstCombine/add.ll b/llvm/test/Transforms/InstCombine/add.ll
--- a/llvm/test/Transforms/InstCombine/add.ll
+++ b/llvm/test/Transforms/InstCombine/add.ll
@@ -2183,7 +2183,7 @@
 ; CHECK-NEXT:    [[M:%.*]] = mul i8 [[X:%.*]], -32
 ; CHECK-NEXT:    [[A:%.*]] = add i8 [[M]], [[Y:%.*]]
 ; CHECK-NEXT:    call void @use(i8 [[A]])
-; CHECK-NEXT:    [[R:%.*]] = trunc i8 [[A]] to i5
+; CHECK-NEXT:    [[R:%.*]] = trunc i8 [[Y]] to i5
 ; CHECK-NEXT:    ret i5 [[R]]
 ;
   %m = mul i8 %x, -32 ; 0xE0
@@ -2193,6 +2193,8 @@
   ret i5 %r
 }
 
+; negative test - demands one more bit
+
 define i6 @demand_low_bits_uses_extra_bit(i8 %x, i8 %y) {
 ; CHECK-LABEL: @demand_low_bits_uses_extra_bit(
 ; CHECK-NEXT:    [[M:%.*]] = mul i8 [[X:%.*]], -32
@@ -2214,7 +2216,7 @@
 ; CHECK-NEXT:    [[M:%.*]] = and i8 [[X:%.*]], -64
 ; CHECK-NEXT:    [[A:%.*]] = add i8 [[Y]], [[M]]
 ; CHECK-NEXT:    call void @use(i8 [[A]])
-; CHECK-NEXT:    [[S:%.*]] = sub i8 [[A]], [[Z:%.*]]
+; CHECK-NEXT:    [[S:%.*]] = sub i8 [[Y]], [[Z:%.*]]
 ; CHECK-NEXT:    [[R:%.*]] = shl i8 [[S]], 2
 ; CHECK-NEXT:    ret i8 [[R]]
 ;
@@ -2227,8 +2229,10 @@
   ret i8 %r
 }
 
-define i8 @demand_low_bits_uses_commutei_extra_bit(i8 %x, i8 %p, i8 %z) {
-; CHECK-LABEL: @demand_low_bits_uses_commutei_extra_bit(
+; negative test - demands one more bit
+
+define i8 @demand_low_bits_uses_commute_extra_bit(i8 %x, i8 %p, i8 %z) {
+; CHECK-LABEL: @demand_low_bits_uses_commute_extra_bit(
 ; CHECK-NEXT:    [[Y:%.*]] = mul i8 [[P:%.*]], [[P]]
 ; CHECK-NEXT:    [[M:%.*]] = and i8 [[X:%.*]], -64
 ; CHECK-NEXT:    [[A:%.*]] = add i8 [[Y]], [[M]]
@@ -2257,7 +2261,7 @@
 ; CHECK-NEXT:    [[XY:%.*]] = or i128 [[SHY]], [[ZX]]
 ; CHECK-NEXT:    [[SUB:%.*]] = sub i128 [[XY]], [[ZZ]]
 ; CHECK-NEXT:    [[ADD:%.*]] = add i128 [[SUB]], [[MW]]
-; CHECK-NEXT:    [[T:%.*]] = trunc i128 [[ADD]] to i64
+; CHECK-NEXT:    [[T:%.*]] = trunc i128 [[SUB]] to i64
 ; CHECK-NEXT:    [[H:%.*]] = lshr i128 [[ADD]], 64
 ; CHECK-NEXT:    [[T2:%.*]] = trunc i128 [[H]] to i64
 ; CHECK-NEXT:    [[R1:%.*]] = insertvalue { i64, i64 } poison, i64 [[T]], 0
diff --git a/llvm/test/Transforms/InstCombine/shift.ll b/llvm/test/Transforms/InstCombine/shift.ll
--- a/llvm/test/Transforms/InstCombine/shift.ll
+++ b/llvm/test/Transforms/InstCombine/shift.ll
@@ -1750,11 +1750,12 @@
 define void @ossfuzz_38078(i32 %arg, i32 %arg1, i32* %ptr, i1* %ptr2, i32* %ptr3, i1* %ptr4, i32* %ptr5, i32* %ptr6, i1* %ptr7) {
 ; CHECK-LABEL: @ossfuzz_38078(
 ; CHECK-NEXT:  bb:
+; CHECK-NEXT:    [[I2:%.*]] = add nsw i32 [[ARG:%.*]], [[ARG1:%.*]]
+; CHECK-NEXT:    [[B3:%.*]] = or i32 [[I2]], 2147483647
 ; CHECK-NEXT:    [[G1:%.*]] = getelementptr i32, i32* [[PTR:%.*]], i64 -1
-; CHECK-NEXT:    [[I2:%.*]] = sub i32 0, [[ARG1:%.*]]
-; CHECK-NEXT:    [[I5:%.*]] = icmp eq i32 [[I2]], [[ARG:%.*]]
+; CHECK-NEXT:    [[I5:%.*]] = icmp eq i32 [[I2]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[I5]])
-; CHECK-NEXT:    store volatile i32 2147483647, i32* [[G1]], align 4
+; CHECK-NEXT:    store volatile i32 [[B3]], i32* [[G1]], align 4
 ; CHECK-NEXT:    br label [[BB:%.*]]
 ; CHECK:       BB:
 ; CHECK-NEXT:    unreachable