diff --git a/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp b/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
@@ -350,8 +350,36 @@
     assert(!LHSKnown.hasConflict() && "Bits known to be one AND zero?");
 
     // If the operands are constants, see if we can simplify them.
-    if (ShrinkDemandedConstant(I, 1, DemandedMask) ||
-        ShrinkDemandedConstant(I, 2, DemandedMask))
+    // This is similar to ShrinkDemandedConstant, but for a select we want to
+    // try to keep the selected constants the same as icmp value constants, if
+    // we can. This helps not break apart (or helps put back together)
+    // canonical patterns like min and max.
+    auto CanonicalizeSelectConstant = [](Instruction *I, unsigned OpNo,
+                                         APInt DemandedMask) {
+      const APInt *SelC;
+      if (!match(I->getOperand(OpNo), m_APInt(SelC)))
+        return false;
+
+      // Get the constant out of the ICmp, if there is one.
+      const APInt *CmpC;
+      ICmpInst::Predicate Pred;
+      if (!match(I->getOperand(0), m_c_ICmp(Pred, m_APInt(CmpC), m_Value())) ||
+          CmpC->getBitWidth() != SelC->getBitWidth())
+        return ShrinkDemandedConstant(I, OpNo, DemandedMask);
+
+      // If the constant is already the same as the ICmp, leave it as-is.
+      if (*CmpC == *SelC)
+        return false;
+      // If the constants are not already the same, but can be with the demand
+      // mask, use the constant value from the ICmp.
+      if ((*CmpC & DemandedMask) == (*SelC & DemandedMask)) {
+        I->setOperand(OpNo, ConstantInt::get(I->getType(), *CmpC));
+        return true;
+      }
+      return ShrinkDemandedConstant(I, OpNo, DemandedMask);
+    };
+    if (CanonicalizeSelectConstant(I, 1, DemandedMask) ||
+        CanonicalizeSelectConstant(I, 2, DemandedMask))
       return I;
 
     // Only known if known in both the LHS and RHS.
diff --git a/llvm/test/Transforms/InstCombine/select-imm-canon.ll b/llvm/test/Transforms/InstCombine/select-imm-canon.ll
--- a/llvm/test/Transforms/InstCombine/select-imm-canon.ll
+++ b/llvm/test/Transforms/InstCombine/select-imm-canon.ll
@@ -4,8 +4,8 @@
 define i8 @single(i32 %A) {
 ; CHECK-LABEL: @single(
 ; CHECK-NEXT:  entry:
-; CHECK-NEXT:    [[L1:%.*]] = icmp slt i32 [[A:%.*]], -128
-; CHECK-NEXT:    [[L2:%.*]] = select i1 [[L1]], i32 128, i32 [[A]]
+; CHECK-NEXT:    [[TMP0:%.*]] = icmp sgt i32 [[A:%.*]], -128
+; CHECK-NEXT:    [[L2:%.*]] = select i1 [[TMP0]], i32 [[A]], i32 -128
 ; CHECK-NEXT:    [[CONV7:%.*]] = trunc i32 [[L2]] to i8
 ; CHECK-NEXT:    ret i8 [[CONV7]]
 ;
@@ -19,10 +19,10 @@
 define i8 @double(i32 %A) {
 ; CHECK-LABEL: @double(
 ; CHECK-NEXT:  entry:
-; CHECK-NEXT:    [[L1:%.*]] = icmp slt i32 [[A:%.*]], -128
-; CHECK-NEXT:    [[L2:%.*]] = select i1 [[L1]], i32 128, i32 [[A]]
-; CHECK-NEXT:    [[DOTINV:%.*]] = icmp sgt i32 [[A]], 127
-; CHECK-NEXT:    [[SPEC_SELECT_I:%.*]] = select i1 [[DOTINV]], i32 127, i32 [[L2]]
+; CHECK-NEXT:    [[TMP0:%.*]] = icmp sgt i32 [[A:%.*]], -128
+; CHECK-NEXT:    [[L2:%.*]] = select i1 [[TMP0]], i32 [[A]], i32 -128
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp slt i32 [[L2]], 127
+; CHECK-NEXT:    [[SPEC_SELECT_I:%.*]] = select i1 [[TMP1]], i32 [[L2]], i32 127
 ; CHECK-NEXT:    [[CONV7:%.*]] = trunc i32 [[SPEC_SELECT_I]] to i8
 ; CHECK-NEXT:    ret i8 [[CONV7]]
 ;
@@ -39,7 +39,7 @@
 ; CHECK-LABEL: @thisdoesnotloop(
 ; CHECK-NEXT:  entry:
 ; CHECK-NEXT:    [[L1:%.*]] = icmp slt i32 [[A:%.*]], -128
-; CHECK-NEXT:    [[L2:%.*]] = select i1 [[L1]], i32 128, i32 [[B:%.*]]
+; CHECK-NEXT:    [[L2:%.*]] = select i1 [[L1]], i32 -128, i32 [[B:%.*]]
 ; CHECK-NEXT:    [[CONV7:%.*]] = trunc i32 [[L2]] to i8
 ; CHECK-NEXT:    ret i8 [[CONV7]]
 ;
@@ -52,10 +52,10 @@
 
 define i8 @original(i32 %A, i32 %B) {
 ; CHECK-LABEL: @original(
-; CHECK-NEXT:    [[TMP1:%.*]] = icmp slt i32 [[A:%.*]], -128
-; CHECK-NEXT:    [[TMP2:%.*]] = select i1 [[TMP1]], i32 128, i32 [[A]]
-; CHECK-NEXT:    [[DOTINV:%.*]] = icmp sgt i32 [[A]], 127
-; CHECK-NEXT:    [[SPEC_SELECT_I:%.*]] = select i1 [[DOTINV]], i32 127, i32 [[TMP2]]
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp sgt i32 [[A:%.*]], -128
+; CHECK-NEXT:    [[TMP2:%.*]] = select i1 [[TMP1]], i32 [[A]], i32 -128
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp slt i32 [[TMP2]], 127
+; CHECK-NEXT:    [[SPEC_SELECT_I:%.*]] = select i1 [[TMP3]], i32 [[TMP2]], i32 127
 ; CHECK-NEXT:    [[CONV7:%.*]] = trunc i32 [[SPEC_SELECT_I]] to i8
 ; CHECK-NEXT:    ret i8 [[CONV7]]
 ;