Index: llvm/trunk/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
===================================================================
--- llvm/trunk/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
+++ llvm/trunk/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
@@ -538,7 +538,7 @@
           SimplifyDemandedBits(I, 0, DemandedFromOps, LHSKnownZero, LHSKnownOne,
                                Depth + 1) ||
           ShrinkDemandedConstant(I, 1, DemandedFromOps) ||
-          SimplifyDemandedBits(I, 1, DemandedFromOps, LHSKnownZero, LHSKnownOne,
+          SimplifyDemandedBits(I, 1, DemandedFromOps, RHSKnownZero, RHSKnownOne,
                                Depth + 1)) {
         // Disable the nsw and nuw flags here: We can no longer guarantee that
         // we won't wrap after simplification. Removing the nsw/nuw flags is
@@ -548,6 +548,15 @@
         BinOP.setHasNoUnsignedWrap(false);
         return I;
       }
+
+      // If we are known to be adding/subtracting zeros to every bit below
+      // the highest demanded bit, we just return the other side.
+      if ((DemandedFromOps & RHSKnownZero) == DemandedFromOps)
+        return I->getOperand(0);
+      // We can't do this with the LHS for subtraction.
+      if (I->getOpcode() == Instruction::Add &&
+          (DemandedFromOps & LHSKnownZero) == DemandedFromOps)
+        return I->getOperand(1);
     }
 
     // Otherwise just hand the add/sub off to computeKnownBits to fill in
Index: llvm/trunk/test/Transforms/InstCombine/and2.ll
===================================================================
--- llvm/trunk/test/Transforms/InstCombine/and2.ll
+++ llvm/trunk/test/Transforms/InstCombine/and2.ll
@@ -122,12 +122,11 @@
   ret i64 %add
 }
 
-; The add in this test is unnecessary because the LSBs of the RHS are 0 and we only consume those bits.
+; The add in this test is unnecessary because the LSBs of the LHS are 0 and the 'and' only consumes bits from those LSBs. It doesn't matter what happens to the upper bits.
 define i32 @test11(i32 %a, i32 %b) {
 ; CHECK-LABEL: @test11(
 ; CHECK-NEXT:    [[X:%.*]] = shl i32 [[A:%.*]], 8
-; CHECK-NEXT:    [[Y:%.*]] = add i32 [[X]], [[B:%.*]]
-; CHECK-NEXT:    [[Z:%.*]] = and i32 [[Y]], 128
+; CHECK-NEXT:    [[Z:%.*]] = and i32 [[B:%.*]], 128
 ; CHECK-NEXT:    [[W:%.*]] = mul i32 [[Z]], [[X]]
 ; CHECK-NEXT:    ret i32 [[W]]
 ;
@@ -138,12 +137,11 @@
   ret i32 %w
 }
 
-; The add in this test is unnecessary because the LSBs of the RHS are 0 and we only consume those bits.
+; The add in this test is unnecessary because the LSBs of the RHS are 0 and the 'and' only consumes bits from those LSBs. It doesn't matter what happens to the upper bits.
 define i32 @test12(i32 %a, i32 %b) {
 ; CHECK-LABEL: @test12(
 ; CHECK-NEXT:    [[X:%.*]] = shl i32 [[A:%.*]], 8
-; CHECK-NEXT:    [[Y:%.*]] = add i32 [[X]], [[B:%.*]]
-; CHECK-NEXT:    [[Z:%.*]] = and i32 [[Y]], 128
+; CHECK-NEXT:    [[Z:%.*]] = and i32 [[B:%.*]], 128
 ; CHECK-NEXT:    [[W:%.*]] = mul i32 [[Z]], [[X]]
 ; CHECK-NEXT:    ret i32 [[W]]
 ;
@@ -154,12 +152,11 @@
   ret i32 %w
 }
 
-; The sub in this test is unnecessary because the LSBs of the RHS are 0 and we only consume those bits.
+; The sub in this test is unnecessary because the LSBs of the RHS are 0 and the 'and' only consumes bits from those LSBs. It doesn't matter what happens to the upper bits.
 define i32 @test13(i32 %a, i32 %b) {
 ; CHECK-LABEL: @test13(
 ; CHECK-NEXT:    [[X:%.*]] = shl i32 [[A:%.*]], 8
-; CHECK-NEXT:    [[Y:%.*]] = sub i32 [[B:%.*]], [[X]]
-; CHECK-NEXT:    [[Z:%.*]] = and i32 [[Y]], 128
+; CHECK-NEXT:    [[Z:%.*]] = and i32 [[B:%.*]], 128
 ; CHECK-NEXT:    [[W:%.*]] = mul i32 [[Z]], [[X]]
 ; CHECK-NEXT:    ret i32 [[W]]
 ;
@@ -170,7 +167,7 @@
   ret i32 %w
 }
 
-; The sub in this test cannot be removed because we need to keep the negation of %b
+; The sub in this test cannot be removed because we need to keep the negation of %b. TODO: But we should be able to replace the LHS of it with a 0.
 define i32 @test14(i32 %a, i32 %b) {
 ; CHECK-LABEL: @test14(
 ; CHECK-NEXT:    [[X:%.*]] = shl i32 [[A:%.*]], 8