Index: llvm/trunk/lib/Analysis/InstructionSimplify.cpp
===================================================================
--- llvm/trunk/lib/Analysis/InstructionSimplify.cpp
+++ llvm/trunk/lib/Analysis/InstructionSimplify.cpp
@@ -1171,6 +1171,11 @@
   if (Op0 == Op1)
     return Constant::getNullValue(Op0->getType());
 
+  // ((X % Y) % Y) -> (X % Y)
+  if (match(Op0, m_SRem(m_Value(), m_Specific(Op1)))) {
+    return Op0;
+  }
+
   // If the operation is with the result of a select instruction, check whether
   // operating on either branch of the select always yields the same value.
   if (isa<SelectInst>(Op0) || isa<SelectInst>(Op1))
Index: llvm/trunk/test/Transforms/InstSimplify/rem.ll
===================================================================
--- llvm/trunk/test/Transforms/InstSimplify/rem.ll
+++ llvm/trunk/test/Transforms/InstSimplify/rem.ll
@@ -15,3 +15,12 @@
   ret i32 %rem
 ; CHECK: ret i32 0
 }
+
+define i32 @select3(i32 %x, i32 %n) {
+; CHECK-LABEL: @select3(
+; CHECK-NEXT: %mod = srem i32 %x, %n
+; CHECK-NEXT: ret i32 %mod
+ %mod = srem i32 %x, %n
+ %mod1 = srem i32 %mod, %n
+ ret i32 %mod1
+}