Index: lib/Transforms/Scalar/IndVarSimplify.cpp
===================================================================
--- lib/Transforms/Scalar/IndVarSimplify.cpp
+++ lib/Transforms/Scalar/IndVarSimplify.cpp
@@ -2724,9 +2724,21 @@
       if (isa<SCEVCouldNotCompute>(ExitCount))
         continue;
 
-      // Better to fold to true (TODO: do so!)
-      if (ExitCount->isZero())
+      // 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.
+      if (ExitCount->isZero()) {
+        auto *BI = cast<BranchInst>(ExitingBB->getTerminator());
+        bool ExitIfTrue = !L->contains(*succ_begin(ExitingBB));
+        auto *NewCond = ExitIfTrue ?
+          ConstantInt::getTrue(BI->getCondition()->getType()) :
+          ConstantInt::getFalse(BI->getCondition()->getType());
+        BI->setCondition(NewCond);
+        Changed = true;
         continue;
+      }
       
       PHINode *IndVar = FindLoopCounter(L, ExitingBB, ExitCount, SE, DT);
       if (!IndVar)
Index: test/Transforms/IndVarSimplify/eliminate-comparison.ll
===================================================================
--- test/Transforms/IndVarSimplify/eliminate-comparison.ll
+++ test/Transforms/IndVarSimplify/eliminate-comparison.ll
@@ -284,7 +284,7 @@
 ; CHECK-NEXT:    [[SEXT21:%.*]] = shl i32 [[TMP57]], 16
 ; CHECK-NEXT:    [[TMP76:%.*]] = icmp ne i32 [[SEXT34]], [[SEXT21]]
 ; CHECK-NEXT:    [[TMP81]] = add nuw nsw i32 [[__KEY8_0]], 1
-; CHECK-NEXT:    br i1 [[TMP76]], label [[FORCOND38]], label [[ASSERT77:%.*]]
+; CHECK-NEXT:    br i1 false, label [[FORCOND38]], label [[ASSERT77:%.*]]
 ; CHECK:       assert77:
 ; CHECK-NEXT:    tail call void @llvm.trap()
 ; CHECK-NEXT:    unreachable
@@ -897,5 +897,4 @@
   ret void
 }
 
-
 !0 = !{i32 0, i32 2147483647}
Index: test/Transforms/IndVarSimplify/eliminate-trunc.ll
===================================================================
--- test/Transforms/IndVarSimplify/eliminate-trunc.ll
+++ test/Transforms/IndVarSimplify/eliminate-trunc.ll
@@ -174,7 +174,7 @@
 ; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i64 [[IV]], 1
 ; CHECK-NEXT:    [[NARROW_IV:%.*]] = trunc i64 [[IV]] to i32
 ; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i32 [[NARROW_IV]], [[N:%.*]]
-; CHECK-NEXT:    br i1 [[CMP]], label [[LOOP]], label [[EXIT:%.*]]
+; CHECK-NEXT:    br i1 false, label [[LOOP]], label [[EXIT:%.*]]
 ; CHECK:       exit:
 ; CHECK-NEXT:    ret void
 ;
@@ -354,7 +354,7 @@
 ; CHECK-NEXT:    [[IV_NEXT]] = add nsw i64 [[IV]], 1
 ; CHECK-NEXT:    [[NARROW_IV:%.*]] = trunc i64 [[IV]] to i32
 ; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 [[NARROW_IV]], [[N:%.*]]
-; CHECK-NEXT:    br i1 [[CMP]], label [[LOOP]], label [[EXIT:%.*]]
+; CHECK-NEXT:    br i1 false, label [[LOOP]], label [[EXIT:%.*]]
 ; CHECK:       exit:
 ; CHECK-NEXT:    ret void
 ;