Index: lib/Transforms/Utils/LoopUnrollPeel.cpp
===================================================================
--- lib/Transforms/Utils/LoopUnrollPeel.cpp
+++ lib/Transforms/Utils/LoopUnrollPeel.cpp
@@ -106,6 +106,40 @@
     }
   }
 
+  // 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 (L->getNumBackEdges() == 1) {
+    BasicBlock *Header = L->getHeader();
+    // Find the only back edge.
+    BasicBlock *BackEdge = nullptr;
+    for (BasicBlock *Pred : predecessors(Header)) {
+      if (L->contains(Pred)) {
+        BackEdge = Pred;
+        break;
+      }
+    }
+    assert(BackEdge && "No back edge in loop?");
+    // 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;
+    }
+  }
+
   return;
 }
 
Index: test/Transforms/LoopUnroll/peel-loop-not-forced.ll
===================================================================
--- /dev/null
+++ test/Transforms/LoopUnroll/peel-loop-not-forced.ll
@@ -0,0 +1,24 @@
+; RUN: opt < %s -S -loop-unroll -indvars -loop-deletion -simplifycfg -instcombine | FileCheck %s
+
+define i32 @invariant_backedge_1(i32 %a, i32 %b) {
+; CHECK-LABEL: @invariant_backedge_1
+; CHECK:       entry:
+; CHECK-NEXT:    %0 = mul i32 %b, 999
+; CHECK-NEXT:    %1 = add i32 %0, %a
+; CHECK-NEXT:    ret i32 %1
+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
+}