Index: lib/Transforms/Utils/LoopUnrollPeel.cpp
===================================================================
--- lib/Transforms/Utils/LoopUnrollPeel.cpp
+++ lib/Transforms/Utils/LoopUnrollPeel.cpp
@@ -71,6 +71,31 @@
   if (!L->empty())
     return;
 
+  // Try to find a Phi node that has the same loop invariant as an input from
+  // its only back edge. If there is such Phi, peeling 1 iteration from the
+  // loop is profitable, because starting from 2nd iteration we will have an
+  // invariant instead of this Phi.
+  if (auto *BackEdge = L->getLoopLatch()) {
+    BasicBlock *Header = L->getHeader();
+    // Iterate over Phis to find one with invariant input on back edge.
+    bool FoundCandidate = false;
+    PHINode *Phi;
+    for (auto BI = Header->begin(); Phi = dyn_cast<PHINode>(&*BI); ++BI) {
+      Value *Input = Phi->getIncomingValueForBlock(BackEdge);
+      if (L->isLoopInvariant(Input)) {
+        FoundCandidate = true;
+        break;
+      }
+    }
+    if (FoundCandidate) {
+      DEBUG(dbgs() << "Peel one iteration to get rid of " << *Phi
+                   << " because starting from 2nd iteration it is always"
+                   << " an invariant\n");
+      UP.PeelCount = 1;
+      return;
+    }
+  }
+
   // Bail if we know the statically calculated trip count.
   // In this case we rather prefer partial unrolling.
   if (TripCount)
Index: test/Transforms/LoopUnroll/peel-loop-not-forced.ll
===================================================================
--- /dev/null
+++ test/Transforms/LoopUnroll/peel-loop-not-forced.ll
@@ -0,0 +1,25 @@
+; RUN: opt < %s -S -loop-unroll | FileCheck %s
+
+define i32 @invariant_backedge_1(i32 %a, i32 %b) {
+; CHECK-LABEL: @invariant_backedge_1
+; CHECK-NOT:     %plus = phi
+; CHECK:       loop.peel:
+; CHECK:       loop:
+; CHECK:         %i = phi
+; CHECK:         %sum = phi
+entry:
+  br label %loop
+
+loop:
+  %i = phi i32 [ 0, %entry ], [ %inc, %loop ]
+  %sum = phi i32 [ 0, %entry ], [ %incsum, %loop ]
+  %plus = phi i32 [ %a, %entry ], [ %b, %loop ]
+
+  %incsum = add i32 %sum, %plus
+  %inc = add i32 %i, 1
+  %cmp = icmp slt i32 %i, 1000
+  br i1 %cmp, label %loop, label %exit
+
+exit:
+  ret i32 %sum
+}