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
@@ -2872,11 +2872,24 @@
     // If X and Y are non-zero then so is X * Y as long as the multiplication
     // does not overflow.
     const OverflowingBinaryOperator *BO = cast<OverflowingBinaryOperator>(V);
-    if ((Q.IIQ.hasNoSignedWrap(BO) || Q.IIQ.hasNoUnsignedWrap(BO)) &&
-        isKnownNonZero(I->getOperand(0), DemandedElts, Depth, Q) &&
-        isKnownNonZero(I->getOperand(1), DemandedElts, Depth, Q))
-      return true;
-    break;
+    if (Q.IIQ.hasNoSignedWrap(BO) || Q.IIQ.hasNoUnsignedWrap(BO))
+      return isKnownNonZero(I->getOperand(0), DemandedElts, Depth, Q) &&
+             isKnownNonZero(I->getOperand(1), DemandedElts, Depth, Q);
+
+    // If either X or Y is odd, then if the other is non-zero the result can't
+    // be zero.
+    KnownBits XKnown =
+        computeKnownBits(I->getOperand(0), DemandedElts, Depth, Q);
+    if (XKnown.One[0])
+      return isKnownNonZero(I->getOperand(1), DemandedElts, Depth, Q);
+
+    KnownBits YKnown =
+        computeKnownBits(I->getOperand(1), DemandedElts, Depth, Q);
+    if (YKnown.One[0])
+      return XKnown.isNonZero() ||
+             isKnownNonZero(I->getOperand(0), DemandedElts, Depth, Q);
+
+    return KnownBits::mul(XKnown, YKnown).isNonZero();
   }
   case Instruction::Select:
     // (C ? X : Y) != 0 if X != 0 and Y != 0.
diff --git a/llvm/test/Analysis/ValueTracking/known-non-zero.ll b/llvm/test/Analysis/ValueTracking/known-non-zero.ll
--- a/llvm/test/Analysis/ValueTracking/known-non-zero.ll
+++ b/llvm/test/Analysis/ValueTracking/known-non-zero.ll
@@ -767,13 +767,9 @@
 
 define i1 @mul_nonzero_odd(i8 %xx, i8 %y, i8 %ind) {
 ; CHECK-LABEL: @mul_nonzero_odd(
-; CHECK-NEXT:    [[XO:%.*]] = or i8 [[XX:%.*]], 1
 ; CHECK-NEXT:    [[Y_NZ:%.*]] = icmp ne i8 [[Y:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[Y_NZ]])
-; CHECK-NEXT:    [[X:%.*]] = mul i8 [[XO]], [[Y]]
-; CHECK-NEXT:    [[Z:%.*]] = or i8 [[X]], [[IND:%.*]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[Z]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %xo = or i8 %xx, 1
   %y_nz = icmp ne i8 %y, 0