diff --git a/src/cmd/compile/internal/ssa/gen/AMD64.rules b/src/cmd/compile/internal/ssa/gen/AMD64.rules
index bda8429c5f..0b02301c7d 100644
--- a/src/cmd/compile/internal/ssa/gen/AMD64.rules
+++ b/src/cmd/compile/internal/ssa/gen/AMD64.rules
@@ -571,6 +571,10 @@
 (SETB (TEST(Q|L|W|B) x x)) -> (ConstBool [0])
 (SETAE (TEST(Q|L|W|B) x x)) -> (ConstBool [1])
 
+// x & 1 != 0 -> x & 1
+(SETNE (TEST(B|W)const [1] x)) => (AND(L|L)const [1] x)
+(SETB (BT(L|Q)const [0] x)) => (AND(L|Q)const [1] x)
+
 // Recognize bit tests: a&(1<<b) != 0 for b suitably bounded
 // Note that BTx instructions use the carry bit, so we need to convert tests for zero flag
 // into tests for carry flags.
diff --git a/src/cmd/compile/internal/ssa/rewriteAMD64.go b/src/cmd/compile/internal/ssa/rewriteAMD64.go
index df36e41d2d..fee9cfee35 100644
--- a/src/cmd/compile/internal/ssa/rewriteAMD64.go
+++ b/src/cmd/compile/internal/ssa/rewriteAMD64.go
@@ -21833,6 +21833,30 @@ func rewriteValueAMD64_OpAMD64SETB(v *Value) bool {
 		v.AuxInt = 0
 		return true
 	}
+	// match: (SETB (BTLconst [0] x))
+	// result: (ANDLconst [1] x)
+	for {
+		if v_0.Op != OpAMD64BTLconst || auxIntToInt8(v_0.AuxInt) != 0 {
+			break
+		}
+		x := v_0.Args[0]
+		v.reset(OpAMD64ANDLconst)
+		v.AuxInt = int32ToAuxInt(1)
+		v.AddArg(x)
+		return true
+	}
+	// match: (SETB (BTQconst [0] x))
+	// result: (ANDQconst [1] x)
+	for {
+		if v_0.Op != OpAMD64BTQconst || auxIntToInt8(v_0.AuxInt) != 0 {
+			break
+		}
+		x := v_0.Args[0]
+		v.reset(OpAMD64ANDQconst)
+		v.AuxInt = int32ToAuxInt(1)
+		v.AddArg(x)
+		return true
+	}
 	// match: (SETB (InvertFlags x))
 	// result: (SETA x)
 	for {
@@ -24176,6 +24200,30 @@ func rewriteValueAMD64_OpAMD64SETLstore(v *Value) bool {
 func rewriteValueAMD64_OpAMD64SETNE(v *Value) bool {
 	v_0 := v.Args[0]
 	b := v.Block
+	// match: (SETNE (TESTBconst [1] x))
+	// result: (ANDLconst [1] x)
+	for {
+		if v_0.Op != OpAMD64TESTBconst || auxIntToInt8(v_0.AuxInt) != 1 {
+			break
+		}
+		x := v_0.Args[0]
+		v.reset(OpAMD64ANDLconst)
+		v.AuxInt = int32ToAuxInt(1)
+		v.AddArg(x)
+		return true
+	}
+	// match: (SETNE (TESTWconst [1] x))
+	// result: (ANDLconst [1] x)
+	for {
+		if v_0.Op != OpAMD64TESTWconst || auxIntToInt16(v_0.AuxInt) != 1 {
+			break
+		}
+		x := v_0.Args[0]
+		v.reset(OpAMD64ANDLconst)
+		v.AuxInt = int32ToAuxInt(1)
+		v.AddArg(x)
+		return true
+	}
 	// match: (SETNE (TESTL (SHLL (MOVLconst [1]) x) y))
 	// result: (SETB (BTL x y))
 	for {
diff --git a/test/codegen/bool.go b/test/codegen/bool.go
new file mode 100644
index 0000000000..929b1b49b9
--- /dev/null
+++ b/test/codegen/bool.go
@@ -0,0 +1,33 @@
+// asmcheck
+
+// Copyright 2020 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package codegen
+
+// This file contains codegen tests related to boolean simplifications/optimizations.
+
+func convertNeq0B(x uint8, c bool) bool {
+	// amd64:"ANDL\t[$]1",-"SETNE"
+	b := x&1 != 0
+	return c && b
+}
+
+func convertNeq0W(x uint16, c bool) bool {
+	// amd64:"ANDL\t[$]1",-"SETNE"
+	b := x&1 != 0
+	return c && b
+}
+
+func convertNeq0L(x uint32, c bool) bool {
+	// amd64:"ANDL\t[$]1",-"SETB"
+	b := x&1 != 0
+	return c && b
+}
+
+func convertNeq0Q(x uint64, c bool) bool {
+	// amd64:"ANDQ\t[$]1",-"SETB"
+	b := x&1 != 0
+	return c && b
+}