diff --git a/lib/Transforms/Utils/SimplifyCFG.cpp b/lib/Transforms/Utils/SimplifyCFG.cpp
index cc28e54c374..2cf4ab9cded 100644
--- a/lib/Transforms/Utils/SimplifyCFG.cpp
+++ b/lib/Transforms/Utils/SimplifyCFG.cpp
@@ -764,12 +764,19 @@ bool llvm::SimplifyCFG(BasicBlock *BB) {
   } else if (UnwindInst *UI = dyn_cast<UnwindInst>(BB->begin())) {
     // Check to see if the first instruction in this block is just an unwind.
     // If so, replace any invoke instructions which use this as an exception
-    // destination with call instructions.
+    // destination with call instructions, and any unconditional branch
+    // predecessor with an unwind.
     //
     std::vector<BasicBlock*> Preds(pred_begin(BB), pred_end(BB));
     while (!Preds.empty()) {
       BasicBlock *Pred = Preds.back();
-      if (InvokeInst *II = dyn_cast<InvokeInst>(Pred->getTerminator()))
+      if (BranchInst *BI = dyn_cast<BranchInst>(Pred->getTerminator())) {
+        if (BI->isUnconditional()) {
+          Pred->getInstList().pop_back();  // nuke uncond branch
+          new UnwindInst(Pred);            // Use unwind.
+          Changed = true;
+        }
+      } else if (InvokeInst *II = dyn_cast<InvokeInst>(Pred->getTerminator()))
         if (II->getUnwindDest() == BB) {
           // Insert a new branch instruction before the invoke, because this
           // is now a fall through...