diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
index 5cb96a2111c7..c6a1328c6b00 100644
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -11742,10 +11742,29 @@ ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
   if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(OrigStart, Stride), OrigRHS))
     BECount = BECountIfBackedgeTaken;
   else {
+    auto canProveRHSGreaterThanEqualStart = [&]() {
+      auto CondGE = IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
+      if (isLoopEntryGuardedByCond(L, CondGE, OrigRHS, OrigStart))
+        return true;
+
+      // (RHS > Start - 1) implies RHS >= Start.
+      // * "RHS >= Start" is trivially equivalent to "RHS > Start - 1" if
+      //   "Start - 1" doesn't overflow.
+      // * For signed comparison, if Start - 1 does overflow, it's equal
+      //   to INT_MAX, and "RHS >s INT_MAX" is trivially false.
+      // * For unsigned comparison, if Start - 1 does overflow, it's equal
+      //   to UINT_MAX, and "RHS >u UINT_MAX" is trivially false.
+      //
+      // FIXME: Should isLoopEntryGuardedByCond do this for us?
+      auto CondGT = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT;
+      auto *StartMinusOne = getAddExpr(OrigStart,
+                                       getMinusOne(OrigStart->getType()));
+      return isLoopEntryGuardedByCond(L, CondGT, OrigRHS, StartMinusOne);
+    };
+
     // If we know that RHS >= Start in the context of loop, then we know that
     // max(RHS, Start) = RHS at this point.
-    if (isLoopEntryGuardedByCond(
-            L, IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, OrigRHS, OrigStart))
+    if (canProveRHSGreaterThanEqualStart())
       End = RHS;
     else
       End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);