diff --git a/lib/Transforms/Scalar/CondPropagate.cpp b/lib/Transforms/Scalar/CondPropagate.cpp
index 2e899432909..f68fb292e4a 100644
--- a/lib/Transforms/Scalar/CondPropagate.cpp
+++ b/lib/Transforms/Scalar/CondPropagate.cpp
@@ -126,6 +126,14 @@ void CondProp::SimplifyPredecessors(BranchInst *BI) {
   // one use (the branch), and is the only instruction besides the branch in the
   // block.
   PHINode *PN = cast<PHINode>(BI->getCondition());
+
+  if (PN->getNumIncomingValues() == 1) {
+    // Eliminate single-entry PHI nodes.
+    FoldSingleEntryPHINodes(PN->getParent());
+    return;
+  }
+  
+  
   if (!PN->hasOneUse()) return;
 
   BasicBlock *BB = BI->getParent();
diff --git a/test/Transforms/CondProp/2009-01-25-SingleEntryPHI.ll b/test/Transforms/CondProp/2009-01-25-SingleEntryPHI.ll
new file mode 100644
index 00000000000..d14ce38f3df
--- /dev/null
+++ b/test/Transforms/CondProp/2009-01-25-SingleEntryPHI.ll
@@ -0,0 +1,37 @@
+; RUN: llvm-as < %s | opt -condprop | llvm-dis
+; PR3405
+target datalayout = "e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128"
+target triple = "x86_64-unknown-linux-gnu"
+
+define i32 @main(i32 %argc, i8** %argv) nounwind {
+entry:
+	br label %bb2
+
+bb2:		; preds = %bb.bb2_crit_edge, %entry
+	br i1 false, label %bb5.thread2, label %bb
+
+bb:		; preds = %bb2
+	br i1 false, label %bb3, label %bb.bb2_crit_edge
+
+bb.bb2_crit_edge:		; preds = %bb
+	br label %bb2
+
+bb3:		; preds = %bb
+	%.lcssa4 = phi i1 [ false, %bb ]		; <i1> [#uses=1]
+	br i1 %.lcssa4, label %bb5.thread, label %bb6
+
+bb5.thread:		; preds = %bb3
+	br label %bb7
+
+bb7:		; preds = %bb5.thread2, %bb5.thread
+	br label %UnifiedReturnBlock
+
+bb6:		; preds = %bb3
+	br label %UnifiedReturnBlock
+
+bb5.thread2:		; preds = %bb2
+	br label %bb7
+
+UnifiedReturnBlock:		; preds = %bb6, %bb7
+	ret i32 0
+}