diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -7635,6 +7635,12 @@
     const SCEV *E, const SCEV *M, bool MaxOrZero,
     ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList)
     : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) {
+  // If we prove the max count is zero, so is the symbolic bound.  This happens
+  // in practice due to differences in a) how context sensitive we've chosen
+  // to be and b) how we reason about bounds impied by UB.
+  if (MaxNotTaken->isZero())
+    ExactNotTaken = MaxNotTaken;
+
   assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
           !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
          "Exact is not allowed to be less precise than Max");
@@ -11939,10 +11945,6 @@
   } else {
     MaxBECount = computeMaxBECountForLT(
         Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
-    // If we prove the max count is zero, so is the symbolic bound.  This can
-    // happen due to differences in how we reason about bounds impied by UB.
-    if (MaxBECount->isZero())
-      BECount = MaxBECount;
   }
 
   if (isa<SCEVCouldNotCompute>(MaxBECount) &&
diff --git a/llvm/lib/Target/ARM/MVETailPredication.cpp b/llvm/lib/Target/ARM/MVETailPredication.cpp
--- a/llvm/lib/Target/ARM/MVETailPredication.cpp
+++ b/llvm/lib/Target/ARM/MVETailPredication.cpp
@@ -293,14 +293,18 @@
     // Check for equality of TC and Ceil by calculating SCEV expression
     // TC - Ceil and test it for zero.
     //
-    bool Zero = SE->getMinusSCEV(
-                      SE->getBackedgeTakenCount(L),
-                      SE->getUDivExpr(SE->getAddExpr(SE->getMulExpr(Ceil, VW),
-                                                     SE->getNegativeSCEV(VW)),
-                                      VW))
-                    ->isZero();
-
-    if (!Zero) {
+    const SCEV *Sub =
+      SE->getMinusSCEV(SE->getBackedgeTakenCount(L),
+                       SE->getUDivExpr(SE->getAddExpr(SE->getMulExpr(Ceil, VW),
+                                                      SE->getNegativeSCEV(VW)),
+                                       VW));
+
+    // Use context sensitive facts about the path to the loop to refine.  This
+    // comes up as the backedge taken count can incorporate context sensitive
+    // reasoning, and our RHS just above doesn't.
+    Sub = SE->applyLoopGuards(Sub, L);
+
+    if (!Sub->isZero()) {
       LLVM_DEBUG(dbgs() << "ARM TP: possible overflow in sub expression.\n");
       return false;
     }
diff --git a/llvm/test/Analysis/ScalarEvolution/max-trip-count.ll b/llvm/test/Analysis/ScalarEvolution/max-trip-count.ll
--- a/llvm/test/Analysis/ScalarEvolution/max-trip-count.ll
+++ b/llvm/test/Analysis/ScalarEvolution/max-trip-count.ll
@@ -523,7 +523,7 @@
 ; of context sensativity.
 define void @ne_zero_max_btc(i32 %a) {
 ; CHECK-LABEL: Determining loop execution counts for: @ne_zero_max_btc
-; CHECK: Loop %for.body: backedge-taken count is (-1 + (zext i32 (1 umax (1 smin %a)) to i64))<nsw>
+; CHECK: Loop %for.body: backedge-taken count is 0
 ; CHECK: Loop %for.body: max backedge-taken count is 0
 entry:
   %cmp = icmp slt i32 %a, 1