diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
index f6c45de9ed62..d48e8a57562c 100644
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -9703,17 +9703,16 @@ const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
   APInt MinStart =
       IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);
 
-  APInt StrideForMaxBECount;
+  APInt StrideForMaxBECount =
+      IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
 
-  bool PositiveStride = isKnownPositive(Stride);
-  if (PositiveStride)
-    StrideForMaxBECount =
-        IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
-  else
-    // Using a stride of 1 is safe when computing max backedge taken count for a
-    // loop with unknown stride, since the precondition for this function is
-    // that it is positive.
-    StrideForMaxBECount = APInt(BitWidth, 1, IsSigned);
+  // We already know that the stride is positive, so we paper over conservatism
+  // in our range computation by forcing StrideForMaxBECount to be at least one.
+  // In theory this is unnecessary, but we expect MaxBECount to be a
+  // SCEVConstant, and (udiv <constant> 0) is not constant folded by SCEV (there
+  // is nothing to constant fold it to).
+  APInt One(BitWidth, 1, IsSigned);
+  StrideForMaxBECount = APIntOps::smax(One, StrideForMaxBECount);
 
   APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth)
                             : APInt::getMaxValue(BitWidth);
diff --git a/llvm/test/Analysis/ScalarEvolution/max-be-count-not-constant.ll b/llvm/test/Analysis/ScalarEvolution/max-be-count-not-constant.ll
new file mode 100644
index 000000000000..b593fc269a7b
--- /dev/null
+++ b/llvm/test/Analysis/ScalarEvolution/max-be-count-not-constant.ll
@@ -0,0 +1,26 @@
+; RUN: opt < %s -analyze -scalar-evolution | FileCheck %s
+
+target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+; Previously in this case the max backedge count would be computed as 1/0, which
+; is correct but undesirable.  It would also not fold as a constant, tripping
+; asserts in SCEV.
+
+define void @pluto(i32 %arg) {
+; CHECK-LABEL: Classifying expressions for: @pluto
+; CHECK: Loop %bb2: max backedge-taken count is 2
+bb:
+  %tmp = ashr i32 %arg, 31
+  %tmp1 = add nsw i32 %tmp, 2
+  br label %bb2
+
+bb2:                                              ; preds = %bb2, %bb
+  %tmp3 = phi i32 [ 0, %bb ], [ %tmp4, %bb2 ]
+  %tmp4 = add nuw nsw i32 %tmp1, %tmp3
+  %tmp5 = icmp ult i32 %tmp4, 2
+  br i1 %tmp5, label %bb2, label %bb6
+
+bb6:                                              ; preds = %bb2
+  ret void
+}