Index: lib/Transforms/InstCombine/InstCombineSelect.cpp
===================================================================
--- lib/Transforms/InstCombine/InstCombineSelect.cpp
+++ lib/Transforms/InstCombine/InstCombineSelect.cpp
@@ -651,24 +651,32 @@
       return ReplaceInstUsesWith(Outer, C);
   }
 
-  // MIN(MIN(A, 23), 97) -> MIN(A, 23)
-  // MAX(MAX(A, 97), 23) -> MAX(A, 97)
   if (SPF1 == SPF2) {
     if (ConstantInt *CB = dyn_cast<ConstantInt>(B)) {
       if (ConstantInt *CC = dyn_cast<ConstantInt>(C)) {
         APInt ACB = CB->getValue();
         APInt ACC = CC->getValue();
+
+        // MIN(MIN(A, 23), 97) -> MIN(A, 23)
+        // MAX(MAX(A, 97), 23) -> MAX(A, 97)
         if ((SPF1 == SPF_UMIN && ACB.ule(ACC)) ||
             (SPF1 == SPF_SMIN && ACB.sle(ACC)) ||
             (SPF1 == SPF_UMAX && ACB.uge(ACC)) ||
             (SPF1 == SPF_SMAX && ACB.sge(ACC)))
           return ReplaceInstUsesWith(Outer, Inner);
+
+        // MIN(MIN(A, 97), 23) -> MIN(A, 23)
+        // MAX(MAX(A, 23), 97) -> MAX(A, 97)
+        if ((SPF1 == SPF_UMIN && ACB.ugt(ACC)) ||
+            (SPF1 == SPF_SMIN && ACB.sgt(ACC)) ||
+            (SPF1 == SPF_UMAX && ACB.ult(ACC)) ||
+            (SPF1 == SPF_SMAX && ACB.slt(ACC))) {
+          Outer.replaceUsesOfWith(Inner, A);
+          return &Outer;
+        }
       }
     }
   }
-
-  // TODO: MIN(MIN(A, 97), 23) -> MIN(A, 23)
-  // TODO: MAX(MAX(A, 23), 97) -> MAX(A, 97)
   return nullptr;
 }
 
Index: test/Transforms/InstCombine/select.ll
===================================================================
--- test/Transforms/InstCombine/select.ll
+++ test/Transforms/InstCombine/select.ll
@@ -1078,4 +1078,56 @@
   ret i32 %retval
 ; CHECK-LABEL: @test71(
 ; CHECK: ret i32 %cond
+}
+
+; SMIN(SMIN(X, 92), 11) -> SMIN(X, 11)
+define i32 @test72(i32 %x) {
+  %cmp = icmp sgt i32 %x, 92
+  %cond = select i1 %cmp, i32 92, i32 %x
+  %cmp3 = icmp sgt i32 %cond, 11
+  %retval = select i1 %cmp3, i32 11, i32 %cond
+  ret i32 %retval
+; CHECK-LABEL: @test72(
+; CHECK-NEXT: [[CMP:%[a-z0-9]+]] = icmp sgt i32 %x, 11
+; CHECK-NEXT: [[SEL:%[a-z0-9]+]] = select i1 [[CMP]], i32 11, i32 %x
+; CHECK-NEXT: ret i32 [[SEL]]
+}
+
+; MIN(MIN(X, 83), 24) -> MIN(X, 24)
+define i32 @test73(i32 %x) {
+  %cmp = icmp ugt i32 %x, 83
+  %cond = select i1 %cmp, i32 83, i32 %x
+  %cmp3 = icmp ugt i32 %cond, 24
+  %retval = select i1 %cmp3, i32 24, i32 %cond
+  ret i32 %retval
+; CHECK-LABEL: @test73(
+; CHECK-NEXT: [[CMP:%[a-z0-9]+]] = icmp ugt i32 %x, 24
+; CHECK-NEXT: [[SEL:%[a-z0-9]+]] = select i1 [[CMP]], i32 24, i32 %x
+; CHECK-NEXT: ret i32 [[SEL]]
+}
+
+; SMAX(SMAX(X, 36), 75) -> SMAX(X, 75)
+define i32 @test74(i32 %x) {
+  %cmp = icmp slt i32 %x, 36
+  %cond = select i1 %cmp, i32 36, i32 %x
+  %cmp3 = icmp slt i32 %cond, 75
+  %retval = select i1 %cmp3, i32 75, i32 %cond
+  ret i32 %retval
+; CHECK-LABEL: @test74(
+; CHECK-NEXT: [[CMP:%[a-z0-9]+]] = icmp slt i32 %x, 75
+; CHECK-NEXT: [[SEL:%[a-z0-9]+]] = select i1 [[CMP]], i32 75, i32 %x
+; CHECK-NEXT: ret i32 [[SEL]]
+}
+
+; MAX(MAX(X, 47), 68) -> MAX(X, 68)
+define i32 @test75(i32 %x) {
+  %cmp = icmp ult i32 %x, 47
+  %cond = select i1 %cmp, i32 47, i32 %x
+  %cmp3 = icmp ult i32 %cond, 68
+  %retval = select i1 %cmp3, i32 68, i32 %cond
+  ret i32 %retval
+; CHECK-LABEL: @test75(
+; CHECK-NEXT: [[CMP:%[a-z0-9]+]] = icmp ult i32 %x, 68
+; CHECK-NEXT: [[SEL:%[a-z0-9]+]] = select i1 [[CMP]], i32 68, i32 %x
+; CHECK-NEXT: ret i32 [[SEL]]
 }
\ No newline at end of file