diff --git a/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp b/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp
--- a/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp
+++ b/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp
@@ -1309,6 +1309,17 @@
   replaceExitCond(BI, NewCond, DeadInsts);
 }
 
+static void replaceLoopPHINodesWithPreheaderValues(
+    Loop *L, SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
+  auto *LoopPreheader = L->getLoopPreheader();
+  auto *LoopHeader = L->getHeader();
+  for (auto &PN : LoopHeader->phis()) {
+    auto *PreheaderIncoming = PN.getIncomingValueForBlock(LoopPreheader);
+    PN.replaceAllUsesWith(PreheaderIncoming);
+    DeadInsts.emplace_back(&PN);
+  }
+}
+
 static void replaceWithInvariantCond(
     const Loop *L, BasicBlock *ExitingBB, ICmpInst::Predicate InvariantPred,
     const SCEV *InvariantLHS, const SCEV *InvariantRHS, SCEVExpander &Rewriter,
@@ -1499,10 +1510,11 @@
     // If we know we'd exit on the first iteration, rewrite the exit to
     // reflect this.  This does not imply the loop must exit through this
     // exit; there may be an earlier one taken on the first iteration.
-    // TODO: Given we know the backedge can't be taken, we should go ahead
-    // and break it.  Or at least, kill all the header phis and simplify.
+    // We know that the backedge can't be taken, so we replace all
+    // the header PHIs with values coming from the preheader.
     if (ExitCount->isZero()) {
       foldExit(L, ExitingBB, true, DeadInsts);
+      replaceLoopPHINodesWithPreheaderValues(L, DeadInsts);
       Changed = true;
       continue;
     }
diff --git a/llvm/test/Transforms/IndVarSimplify/eliminate-backedge.ll b/llvm/test/Transforms/IndVarSimplify/eliminate-backedge.ll
--- a/llvm/test/Transforms/IndVarSimplify/eliminate-backedge.ll
+++ b/llvm/test/Transforms/IndVarSimplify/eliminate-backedge.ll
@@ -15,16 +15,13 @@
 ; CHECK:       loop_preheader:
 ; CHECK-NEXT:    br label %loop
 ; CHECK:       loop:
-; CHECK-NEXT:    %iv = phi i32 [ 0, %loop_preheader ], [ %iv.next, %exiting_3 ]
-; CHECK-NEXT:    %iv.wide = phi i64 [ 0, %loop_preheader ], [ %iv.wide.next, %exiting_3 ]
-; CHECK-NEXT:    %iv.next = add nuw nsw i32 %iv, 1
-; CHECK-NEXT:    %iv.wide.next = add nuw nsw i64 %iv.wide, 1
-; CHECK-NEXT:    %left_ptr = getelementptr inbounds i8, i8* %lhs, i32 %iv
-; CHECK-NEXT:    %right_ptr = getelementptr inbounds i8, i8* %rhs, i32 %iv
+; CHECK-NEXT:    %iv.next = add nuw nsw i32 0, 1
+; CHECK-NEXT:    %left_ptr = getelementptr inbounds i8, i8* %lhs, i32 0
+; CHECK-NEXT:    %right_ptr = getelementptr inbounds i8, i8* %rhs, i32 0
 ; CHECK-NEXT:    %result = call i1 @foo(i8* %left_ptr, i8* %right_ptr)
 ; CHECK-NEXT:    br i1 %result, label %exiting_1, label %exit.loopexit
 ; CHECK:       exiting_1:
-; CHECK-NEXT:    %iv.wide.is_not_zero = icmp ne i64 %iv.wide, 0
+; CHECK-NEXT:    %iv.wide.is_not_zero = icmp ne i64 0, 0
 ; CHECK-NEXT:    br i1 false, label %exiting_2, label %exit.loopexit
 ; CHECK:       exiting_2:
 ; CHECK-NEXT:    %bar_ret = call i1 @bar()
diff --git a/llvm/test/Transforms/IndVarSimplify/eliminate-exit-no-dl.ll b/llvm/test/Transforms/IndVarSimplify/eliminate-exit-no-dl.ll
--- a/llvm/test/Transforms/IndVarSimplify/eliminate-exit-no-dl.ll
+++ b/llvm/test/Transforms/IndVarSimplify/eliminate-exit-no-dl.ll
@@ -14,10 +14,9 @@
 ; CHECK-NEXT:  bb:
 ; CHECK-NEXT:    br label [[BB3:%.*]]
 ; CHECK:       bb3:
-; CHECK-NEXT:    [[TMP:%.*]] = phi i8* [ [[TMP4:%.*]], [[BB7:%.*]] ], [ getelementptr inbounds ([0 x i8], [0 x i8]* @global, i64 0, i64 2), [[BB:%.*]] ]
-; CHECK-NEXT:    [[TMP4]] = getelementptr inbounds i8, i8* [[TMP]], i64 -1
+; CHECK-NEXT:    [[TMP4:%.*]] = getelementptr inbounds i8, i8* getelementptr inbounds ([0 x i8], [0 x i8]* @global, i64 0, i64 2), i64 -1
 ; CHECK-NEXT:    [[TMP6:%.*]] = load i8, i8* [[TMP4]], align 1
-; CHECK-NEXT:    br i1 false, label [[BB7]], label [[BB11:%.*]]
+; CHECK-NEXT:    br i1 false, label [[BB7:%.*]], label [[BB11:%.*]]
 ; CHECK:       bb7:
 ; CHECK-NEXT:    [[TMP8:%.*]] = zext i8 [[TMP6]] to i64
 ; CHECK-NEXT:    br i1 true, label [[BB11]], label [[BB3]]
diff --git a/llvm/test/Transforms/IndVarSimplify/floating-point-iv.ll b/llvm/test/Transforms/IndVarSimplify/floating-point-iv.ll
--- a/llvm/test/Transforms/IndVarSimplify/floating-point-iv.ll
+++ b/llvm/test/Transforms/IndVarSimplify/floating-point-iv.ll
@@ -65,9 +65,7 @@
 ; CHECK-NEXT:  entry:
 ; CHECK-NEXT:    br label [[BB:%.*]]
 ; CHECK:       bb:
-; CHECK-NEXT:    [[IV:%.*]] = phi double [ 0.000000e+00, [[ENTRY:%.*]] ], [ [[TMP1:%.*]], [[BB]] ]
-; CHECK-NEXT:    [[TMP0:%.*]] = tail call i32 @foo(double [[IV]]) #[[ATTR0]]
-; CHECK-NEXT:    [[TMP1]] = fadd double [[IV]], 1.000000e+00
+; CHECK-NEXT:    [[TMP0:%.*]] = tail call i32 @foo(double 0.000000e+00) #[[ATTR0]]
 ; CHECK-NEXT:    br i1 false, label [[BB]], label [[RETURN:%.*]]
 ; CHECK:       return:
 ; CHECK-NEXT:    ret void