diff --git a/llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp b/llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp
@@ -2984,6 +2984,14 @@
   if (match(CondVal, m_Select(m_Value(A), m_Value(B), m_Zero())) &&
       match(TrueVal, m_Specific(B)) && match(FalseVal, m_Zero()))
     return replaceOperand(SI, 0, A);
+  // select a, (select ~a, true, b), false -> select a, b, false
+  if (match(TrueVal, m_c_LogicalOr(m_Not(m_Specific(CondVal)), m_Value(B))) &&
+      match(FalseVal, m_Zero()))
+    return replaceOperand(SI, 1, B);
+  // select a, true, (select ~a, b, false) -> select a, true, b
+  if (match(FalseVal, m_c_LogicalAnd(m_Not(m_Specific(CondVal)), m_Value(B))) &&
+      match(TrueVal, m_One()))
+    return replaceOperand(SI, 2, B);
 
   // ~(A & B) & (A | B) --> A ^ B
   if (match(&SI, m_c_LogicalAnd(m_Not(m_LogicalAnd(m_Value(A), m_Value(B))),
diff --git a/llvm/test/Transforms/InstCombine/logical-select.ll b/llvm/test/Transforms/InstCombine/logical-select.ll
--- a/llvm/test/Transforms/InstCombine/logical-select.ll
+++ b/llvm/test/Transforms/InstCombine/logical-select.ll
@@ -1121,3 +1121,131 @@
   call void @use1(i1 %and1)
   ret i1 %r
 }
+
+; A & (~A | B) --> A & B
+define i1 @and_commute1(i1 %a, i1 %b) {
+; CHECK-LABEL: @and_commute1(
+; CHECK-NEXT:    [[AND:%.*]] = select i1 [[A:%.*]], i1 [[B:%.*]], i1 false
+; CHECK-NEXT:    ret i1 [[AND]]
+;
+  %not = xor i1 %a, true
+  %or = or i1 %not, %b
+  %and = select i1 %a, i1 %or, i1 zeroinitializer
+  ret i1 %and
+}
+
+; A & (~A | B) --> A & B
+define <2 x i1> @and_commute1_vec(<2 x i1> %a, <2 x i1> %b) {
+; CHECK-LABEL: @and_commute1_vec(
+; CHECK-NEXT:    [[AND:%.*]] = select <2 x i1> [[A:%.*]], <2 x i1> [[B:%.*]], <2 x i1> zeroinitializer
+; CHECK-NEXT:    ret <2 x i1> [[AND]]
+;
+  %not = xor <2 x i1> %a, <i1 true, i1 true>
+  %or = or <2 x i1> %not, %b
+  %and = select <2 x i1> %a, <2 x i1> %or, <2 x i1> zeroinitializer
+  ret <2 x i1> %and
+}
+
+; A & (~A | B) --> A & B
+define i1 @and_commute2(i1 %a, i1 %b) {
+; CHECK-LABEL: @and_commute2(
+; CHECK-NEXT:    [[AND:%.*]] = select i1 [[A:%.*]], i1 [[B:%.*]], i1 false
+; CHECK-NEXT:    ret i1 [[AND]]
+;
+  %not = xor i1 %a, true
+  %or = select i1 %not, i1 true, i1 %b
+  %and = select i1 %a, i1 %or, i1 zeroinitializer
+  ret i1 %and
+}
+
+; A & (~A | B) --> A & B
+define <2 x i1> @and_commute2_vec(<2 x i1> %a, <2 x i1> %b) {
+; CHECK-LABEL: @and_commute2_vec(
+; CHECK-NEXT:    [[AND:%.*]] = select <2 x i1> [[A:%.*]], <2 x i1> [[B:%.*]], <2 x i1> zeroinitializer
+; CHECK-NEXT:    ret <2 x i1> [[AND]]
+;
+  %not = xor <2 x i1> %a, <i1 true, i1 true>
+  %or = select <2 x i1> %not, <2 x i1> <i1 true, i1 true>, <2 x i1> %b
+  %and = select <2 x i1> %a, <2 x i1> %or, <2 x i1> zeroinitializer
+  ret <2 x i1> %and
+}
+
+; A & (~A | B) --> A & B
+; As and_commute1 but with %or's operands switched
+define i1 @and_commute3(i1 %a) {
+; CHECK-LABEL: @and_commute3(
+; CHECK-NEXT:    [[B:%.*]] = call i1 @gen()
+; CHECK-NEXT:    [[AND:%.*]] = select i1 [[A:%.*]], i1 [[B]], i1 false
+; CHECK-NEXT:    ret i1 [[AND]]
+;
+  %b = call i1 @gen()
+  %not = xor i1 %a, true
+  %or = or i1 %b, %not
+  %and = select i1 %a, i1 %or, i1 zeroinitializer
+  ret i1 %and
+}
+
+; A | (~A & B) -> A | B
+define i1 @or_commute1(i1 %a, i1 %b) {
+; CHECK-LABEL: @or_commute1(
+; CHECK-NEXT:    [[OR:%.*]] = select i1 [[A:%.*]], i1 true, i1 [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[OR]]
+;
+  %not = xor i1 %a, true
+  %and = and i1 %not, %b
+  %or = select i1 %a, i1 true, i1 %and
+  ret i1 %or
+}
+
+; A | (~A & B) -> A | B
+define <2 x i1> @or_commute1_vec(<2 x i1> %a, <2 x i1> %b) {
+; CHECK-LABEL: @or_commute1_vec(
+; CHECK-NEXT:    [[OR:%.*]] = select <2 x i1> [[A:%.*]], <2 x i1> <i1 true, i1 true>, <2 x i1> [[B:%.*]]
+; CHECK-NEXT:    ret <2 x i1> [[OR]]
+;
+  %not = xor <2 x i1> %a, <i1 true, i1 true>
+  %and = and <2 x i1> %not, %b
+  %or = select <2 x i1> %a, <2 x i1> <i1 true, i1 true>, <2 x i1> %and
+  ret <2 x i1> %or
+}
+
+; A | (~A & B) -> A | B
+define i1 @or_commute2(i1 %a, i1 %b) {
+; CHECK-LABEL: @or_commute2(
+; CHECK-NEXT:    [[OR:%.*]] = select i1 [[A:%.*]], i1 true, i1 [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[OR]]
+;
+  %not = xor i1 %a, true
+  %and = select i1 %not, i1 %b, i1 false
+  %or = select i1 %a, i1 true, i1 %and
+  ret i1 %or
+}
+
+; A | (~A & B) -> A | B
+define <2 x i1> @or_commute2_vec(<2 x i1> %a, <2 x i1> %b) {
+; CHECK-LABEL: @or_commute2_vec(
+; CHECK-NEXT:    [[OR:%.*]] = select <2 x i1> [[A:%.*]], <2 x i1> <i1 true, i1 true>, <2 x i1> [[B:%.*]]
+; CHECK-NEXT:    ret <2 x i1> [[OR]]
+;
+  %not = xor <2 x i1> %a, <i1 true, i1 true>
+  %and = select <2 x i1> %not, <2 x i1> %b, <2 x i1> zeroinitializer
+  %or = select <2 x i1> %a, <2 x i1> <i1 true, i1 true>, <2 x i1> %and
+  ret <2 x i1> %or
+}
+
+; A | (~A & B) -> A | B
+; As or_commute1 but with %and's operands switched
+define i1 @or_commute3(i1 %a) {
+; CHECK-LABEL: @or_commute3(
+; CHECK-NEXT:    [[B:%.*]] = call i1 @gen()
+; CHECK-NEXT:    [[OR:%.*]] = select i1 [[A:%.*]], i1 true, i1 [[B]]
+; CHECK-NEXT:    ret i1 [[OR]]
+;
+  %b = call i1 @gen()
+  %not = xor i1 %a, true
+  %and = and i1 %b, %not
+  %or = select i1 %a, i1 true, i1 %and
+  ret i1 %or
+}
+
+declare i1 @gen()