diff --git a/src/cmd/compile/internal/ssa/prove.go b/src/cmd/compile/internal/ssa/prove.go
index dcdb48180c9..c5387802a79 100644
--- a/src/cmd/compile/internal/ssa/prove.go
+++ b/src/cmd/compile/internal/ssa/prove.go
@@ -1296,6 +1296,13 @@ func removeBranch(b *Block, branch branch) {
 
 // isNonNegative reports whether v is known to be greater or equal to zero.
 func isNonNegative(v *Value) bool {
+	if !v.Type.IsInteger() {
+		panic("isNonNegative bad type")
+	}
+	if !v.Type.IsSigned() {
+		return true
+	}
+
 	switch v.Op {
 	case OpConst64:
 		return v.AuxInt >= 0
@@ -1303,16 +1310,37 @@ func isNonNegative(v *Value) bool {
 	case OpConst32:
 		return int32(v.AuxInt) >= 0
 
+	case OpConst16:
+		return int16(v.AuxInt) >= 0
+
+	case OpConst8:
+		return int8(v.AuxInt) >= 0
+
 	case OpStringLen, OpSliceLen, OpSliceCap,
-		OpZeroExt8to64, OpZeroExt16to64, OpZeroExt32to64:
+		OpZeroExt8to64, OpZeroExt16to64, OpZeroExt32to64,
+		OpZeroExt8to32, OpZeroExt16to32, OpZeroExt8to16,
+		OpCtz64, OpCtz32, OpCtz16, OpCtz8:
 		return true
 
-	case OpRsh64Ux64:
+	case OpRsh64Ux64, OpRsh32Ux64:
 		by := v.Args[1]
 		return by.Op == OpConst64 && by.AuxInt > 0
 
-	case OpRsh64x64:
+	case OpRsh64x64, OpRsh32x64, OpRsh8x64, OpRsh16x64, OpRsh32x32, OpRsh64x32,
+		OpSignExt32to64, OpSignExt16to64, OpSignExt8to64, OpSignExt16to32, OpSignExt8to32:
 		return isNonNegative(v.Args[0])
+
+	case OpAnd64, OpAnd32, OpAnd16, OpAnd8:
+		return isNonNegative(v.Args[0]) || isNonNegative(v.Args[1])
+
+	case OpMod64, OpMod32, OpMod16, OpMod8,
+		OpDiv64, OpDiv32, OpDiv16, OpDiv8,
+		OpOr64, OpOr32, OpOr16, OpOr8,
+		OpXor64, OpXor32, OpXor16, OpXor8:
+		return isNonNegative(v.Args[0]) && isNonNegative(v.Args[1])
+
+		// We could handle OpPhi here, but the improvements from doing
+		// so are very minor, and it is neither simple nor cheap.
 	}
 	return false
 }