diff --git a/llvm/include/llvm/Analysis/ScalarEvolution.h b/llvm/include/llvm/Analysis/ScalarEvolution.h
--- a/llvm/include/llvm/Analysis/ScalarEvolution.h
+++ b/llvm/include/llvm/Analysis/ScalarEvolution.h
@@ -1811,7 +1811,7 @@
   /// SCEV predicates in order to return an exact answer.
   ExitLimit howManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
                              bool isSigned, bool ControlsExit,
-                             bool AllowPredicates = false);
+                             bool AllowPredicates, ICmpInst *OrigCond);
 
   ExitLimit howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
                                 bool isSigned, bool IsSubExpr,
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
@@ -8108,7 +8108,7 @@
   case ICmpInst::ICMP_ULT: {                    // while (X < Y)
     bool IsSigned = Pred == ICmpInst::ICMP_SLT;
     ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
-                                    AllowPredicates);
+                                    AllowPredicates, ExitCond);
     if (EL.hasAnyInfo()) return EL;
     break;
   }
@@ -11573,7 +11573,8 @@
 ScalarEvolution::ExitLimit
 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
                                   const Loop *L, bool IsSigned,
-                                  bool ControlsExit, bool AllowPredicates) {
+                                  bool ControlsExit, bool AllowPredicates,
+                                  ICmpInst *OrigCond) {
   SmallPtrSet<const SCEVPredicate *, 4> Predicates;
 
   const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
@@ -11765,8 +11766,23 @@
   const SCEV *BECount = nullptr;
   auto *StartMinusStride = getMinusSCEV(OrigStart, Stride);
   // Can we prove (max(RHS,Start) > Start - Stride?
-  if (isLoopEntryGuardedByCond(L, Cond, StartMinusStride, Start) &&
-      isLoopEntryGuardedByCond(L, Cond, StartMinusStride, RHS)) {
+  if (isLoopEntryGuardedByCond(L, Cond, StartMinusStride, RHS)) {
+    auto MaySubOverflow = [&]() {
+      // Start - Stride < Start implies no overflow.
+      if (isLoopEntryGuardedByCond(L, Cond, StartMinusStride, Start))
+        return false;
+      // Check if we have an IR instruction feeding into the branch
+      // "add nsw IVMinusStride, Stride"
+      if (getSCEV(OrigCond->getOperand(0)) == IV) {
+        if (auto *Add = dyn_cast<AddOperator>(OrigCond->getOperand(0))) {
+          if (IsSigned ? Add->hasNoSignedWrap() : Add->hasNoUnsignedWrap()) {
+            if (getSCEV(Add->getOperand(1)) == Stride)
+              return false;
+          }
+        }
+      }
+      return true;
+    };
     // In this case, we can use a refined formula for computing backedge taken
     // count.  The general formula remains:
     //   "End-Start /uceiling Stride" where "End = max(RHS,Start)"
@@ -11785,11 +11801,13 @@
     //   "((RHS - 1) - (Start - Stride)) /u Stride" reassociates to
     //   "((RHS - (Start - Stride) - 1) /u Stride".
     //   Our preconditions trivially imply no overflow in that form.
-    const SCEV *MinusOne = getMinusOne(Stride->getType());
-    const SCEV *Numerator =
-        getMinusSCEV(getAddExpr(RHS, MinusOne), StartMinusStride);
-    if (!isa<SCEVCouldNotCompute>(Numerator)) {
-      BECount = getUDivExpr(Numerator, Stride);
+    if (!MaySubOverflow()) {
+      const SCEV *MinusOne = getMinusOne(Stride->getType());
+      const SCEV *Numerator =
+          getMinusSCEV(getAddExpr(RHS, MinusOne), StartMinusStride);
+      if (!isa<SCEVCouldNotCompute>(Numerator)) {
+        BECount = getUDivExpr(Numerator, Stride);
+      }
     }
   }
 
diff --git a/llvm/test/Analysis/ScalarEvolution/trip-count-unknown-stride.ll b/llvm/test/Analysis/ScalarEvolution/trip-count-unknown-stride.ll
--- a/llvm/test/Analysis/ScalarEvolution/trip-count-unknown-stride.ll
+++ b/llvm/test/Analysis/ScalarEvolution/trip-count-unknown-stride.ll
@@ -5,7 +5,7 @@
 ; that this is not an infinite loop with side effects.
 
 ; CHECK-LABEL: Determining loop execution counts for: @foo1
-; CHECK: backedge-taken count is ((-1 + (%n smax %s)) /u %s)
+; CHECK: backedge-taken count is ((-1 + %n) /u %s)
 
 ; We should have a conservative estimate for the max backedge taken count for
 ; loops with unknown stride.