diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -6453,15 +6453,19 @@
         if (SA->getValue().uge(BitWidth))
           break;
 
-        // It is currently not resolved how to interpret NSW for left
-        // shift by BitWidth - 1, so we avoid applying flags in that
-        // case. Remove this check (or this comment) once the situation
-        // is resolved. See
-        // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
-        // and http://reviews.llvm.org/D8890 .
+        // We can safely preserve the nuw flag in all cases. It's also safe to
+        // turn a nuw nsw shl into a nuw nsw mul. However, nsw in isolation
+        // requires special handling. It can be preserved as long as we're not
+        // left shifting by bitwidth - 1.
         auto Flags = SCEV::FlagAnyWrap;
-        if (BO->Op && SA->getValue().ult(BitWidth - 1))
-          Flags = getNoWrapFlagsFromUB(BO->Op);
+        if (BO->Op) {
+          auto MulFlags = getNoWrapFlagsFromUB(BO->Op);
+          if ((MulFlags & SCEV::FlagNSW) &&
+              ((MulFlags & SCEV::FlagNUW) || SA->getValue().ult(BitWidth - 1)))
+            Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNSW);
+          if (MulFlags & SCEV::FlagNUW)
+            Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNUW);
+        }
 
         Constant *X = ConstantInt::get(
             getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
diff --git a/llvm/test/Analysis/ScalarEvolution/flags-from-poison.ll b/llvm/test/Analysis/ScalarEvolution/flags-from-poison.ll
--- a/llvm/test/Analysis/ScalarEvolution/flags-from-poison.ll
+++ b/llvm/test/Analysis/ScalarEvolution/flags-from-poison.ll
@@ -559,11 +559,11 @@
   %i = phi i32 [ %nexti, %loop ], [ %start, %entry ]
 
 ; CHECK: %index32 =
-; CHECK: --> {(-2147483648 * %start),+,-2147483648}<%loop>
+; CHECK: --> {(-2147483648 * %start),+,-2147483648}<nsw><%loop>
   %index32 = shl nuw nsw i32 %i, 31
 
 ; CHECK: %index64 =
-; CHECK: --> (sext i32 {(-2147483648 * %start),+,-2147483648}<%loop>
+; CHECK: --> {(sext i32 (-2147483648 * %start) to i64),+,-2147483648}<nsw><%loop>
   %index64 = sext i32 %index32 to i64
 
   %ptr = getelementptr inbounds float, float* %input, i64 %index64