Index: lib/Transforms/InstCombine/InstCombineCompares.cpp
===================================================================
--- lib/Transforms/InstCombine/InstCombineCompares.cpp
+++ lib/Transforms/InstCombine/InstCombineCompares.cpp
@@ -1966,6 +1966,15 @@
     return new ICmpInst(Pred, Builder->CreateTrunc(X, TruncTy), NewC);
   }
 
+  // when the shift is nuw and pred is >u or <=, then comparison only really
+  // happens in the pre-shifted bits.
+  if (Shl->hasNoUnsignedWrap() &&
+      (Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_ULE)) {
+    Type *CTy = IntegerType::get(Cmp.getContext(), C->getBitWidth());
+    Value *NewC = ConstantInt::get(CTy, C->lshr(*ShiftAmt));
+    return new ICmpInst(Pred, X, NewC);
+  }
+
   return nullptr;
 }
 
Index: test/Transforms/InstCombine/icmp-shl-zext-simplify.ll
===================================================================
--- /dev/null
+++ test/Transforms/InstCombine/icmp-shl-zext-simplify.ll
@@ -0,0 +1,73 @@
+; RUN: opt %s -instcombine -S | FileCheck %s
+
+define i32 @icmp_ugt_16(i16) {
+; CHECK-LABEL: @icmp_ugt_16
+; CHECK-NEXT: icmp ne i16 %0, 0
+; CHECK-NEXT: zext
+; CHECK-NEXT: ret
+  %b = zext i16 %0 to i64
+  %c = shl i64 %b, 16
+  %d = icmp ugt i64 %c, 65535
+  %rv = zext i1 %d to i32
+  ret i32 %rv
+}
+
+define i32 @icmp_ule_16(i16) {
+; CHECK-LABEL: @icmp_ule_16
+; CHECK-NEXT: icmp eq i16 %0, 0
+; CHECK-NEXT: zext
+; CHECK-NEXT: ret
+  %b = zext i16 %0 to i64
+  %c = shl i64 %b, 16
+  %d = icmp ule i64 %c, 65535
+  %rv = zext i1 %d to i32
+  ret i32 %rv
+}
+
+define i32 @icmp_ugt_32(i32) {
+; CHECK-LABEL: @icmp_ugt_32
+; CHECK-NEXT: icmp ne i32 %0, 0
+; CHECK-NEXT: zext
+; CHECK-NEXT: ret
+  %b = zext i32 %0 to i64
+  %c = shl i64 %b, 32
+  %d = icmp ugt i64 %c, 4294967295
+  %rv = zext i1 %d to i32
+  ret i32 %rv
+}
+
+define i32 @icmp_ule_32(i32) {
+; CHECK-LABEL: @icmp_ule_32
+; CHECK-NEXT: icmp eq i32 %0, 0
+; CHECK-NEXT: zext
+; CHECK-NEXT: ret
+  %b = zext i32 %0 to i64
+  %c = shl i64 %b, 32
+  %d = icmp ule i64 %c, 4294967295
+  %rv = zext i1 %d to i32
+  ret i32 %rv
+}
+
+define i32 @icmp_ugt_64(i64) {
+; CHECK-LABEL: @icmp_ugt_64
+; CHECK-NEXT: icmp ne i64 %0, 0
+; CHECK-NEXT: zext
+; CHECK-NEXT: ret
+  %b = zext i64 %0 to i128
+  %c = shl i128 %b, 64
+  %d = icmp ugt i128 %c, 18446744073709551615
+  %rv = zext i1 %d to i32
+  ret i32 %rv
+}
+
+define i32 @icmp_ule_64(i64) {
+; CHECK-LABEL: @icmp_ule_64
+; CHECK-NEXT: icmp eq i64 %0, 0
+; CHECK-NEXT: zext
+; CHECK-NEXT: ret
+  %b = zext i64 %0 to i128
+  %c = shl i128 %b, 64
+  %d = icmp ule i128 %c, 18446744073709551615
+  %rv = zext i1 %d to i32
+  ret i32 %rv
+}