Index: lib/Transforms/InstCombine/InstCombineSelect.cpp
===================================================================
--- lib/Transforms/InstCombine/InstCombineSelect.cpp
+++ lib/Transforms/InstCombine/InstCombineSelect.cpp
@@ -66,7 +66,8 @@
     }
   }
 
-  // TODO: (X > 4) ? X : 5   -->  (X >= 5) ? X : 5  -->  MAX(X, 5)
+  // (X > 4) ? X : 5   -->  (X >= 5) ? X : 5  -->  MAX(X, 5)
+  // Handled in visitSelectInstWithICmp())
 
   return SPF_UNKNOWN;
 }
@@ -651,11 +652,30 @@
       return ReplaceInstUsesWith(Outer, C);
   }
 
-  // TODO: MIN(MIN(A, 23), 97)
+  // MIN(MIN(A, 23), 97) -> MIN(A, 23)
+  // MAX(MAX(A, 97), 23) -> MAX(A, 97)
+  if (SPF1 == SPF2 && isa<Constant>(B) && isa<Constant>(C)) {
+    unsigned short Pred;
+    switch (SPF1) {
+    default:       Pred = ICmpInst::BAD_ICMP_PREDICATE;
+    case SPF_SMIN: Pred = ICmpInst::ICMP_SLE; break;
+    case SPF_UMIN: Pred = ICmpInst::ICMP_ULE; break;
+    case SPF_SMAX: Pred = ICmpInst::ICMP_SGE; break;
+    case SPF_UMAX: Pred = ICmpInst::ICMP_UGE; break;
+    }
+
+    if (Pred != ICmpInst::BAD_ICMP_PREDICATE) {
+      Constant *CB = cast<Constant>(B);
+      Constant *CC = cast<Constant>(C);
+      Constant *IsCPredB = ConstantExpr::getICmp(Pred, CC, CB);
+      if (IsCPredB && IsCPredB->isZeroValue()) {
+        return ReplaceInstUsesWith(Outer, Inner);
+      }
+    }
+  }
   return nullptr;
 }
 
-
 /// foldSelectICmpAnd - If one of the constants is zero (we know they can't
 /// both be) and we have an icmp instruction with zero, and we have an 'and'
 /// with the non-constant value and a power of two we can turn the select
Index: test/Transforms/InstCombine/select.ll
===================================================================
--- test/Transforms/InstCombine/select.ll
+++ test/Transforms/InstCombine/select.ll
@@ -1031,3 +1031,51 @@
 ; CHECK: lshr exact i32 %2, 1
 ; CHECK: xor i32 %3, 42
 }
+
+; SMIN(SMIN(X, 11), 92) -> SMIN(X, 11)
+define i32 @test68(i32 %x) {
+entry:
+  %cmp = icmp slt i32 11, %x
+  %cond = select i1 %cmp, i32 11, i32 %x
+  %cmp3 = icmp slt i32 92, %cond
+  %retval = select i1 %cmp3, i32 92, i32 %cond
+  ret i32 %retval
+; CHECK-LABEL: @test68(
+; CHECK: ret i32 %cond
+}
+
+; MIN(MIN(X, 24), 83) -> MIN(X, 24)
+define i32 @test69(i32 %x) {
+entry:
+  %cmp = icmp ult i32 24, %x
+  %cond = select i1 %cmp, i32 24, i32 %x
+  %cmp3 = icmp ult i32 83, %cond
+  %retval = select i1 %cmp3, i32 83, i32 %cond
+  ret i32 %retval
+; CHECK-LABEL: @test69(
+; CHECK: ret i32 %cond
+}
+
+; SMAX(SMAX(X, 75), 36) -> SMAX(X, 75)
+define i32 @test70(i32 %x) {
+entry:
+  %cmp = icmp slt i32 %x, 75
+  %cond = select i1 %cmp, i32 75, i32 %x
+  %cmp3 = icmp slt i32 %cond, 36
+  %retval = select i1 %cmp3, i32 36, i32 %cond
+  ret i32 %retval
+; CHECK-LABEL: @test70(
+; CHECK: ret i32 %cond
+}
+
+; MAX(MAX(X, 68), 47) -> MAX(X, 68)
+define i32 @test71(i32 %x) {
+entry:
+  %cmp = icmp ult i32 %x, 68
+  %cond = select i1 %cmp, i32 68, i32 %x
+  %cmp3 = icmp ult i32 %cond, 47
+  %retval = select i1 %cmp3, i32 47, i32 %cond
+  ret i32 %retval
+; CHECK-LABEL: @test71(
+; CHECK: ret i32 %cond
+}
\ No newline at end of file