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
@@ -10628,8 +10628,15 @@
 
   const SCEV *Start = IV->getStart();
   const SCEV *End = RHS;
-  if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
-    End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
+  if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
+    // If we know that Start >= RHS in the context of loop, then we know that
+    // min(RHS, Start) = RHS at this point.
+    if (isLoopEntryGuardedByCond(
+            L, IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, Start, RHS))
+      End = RHS;
+    else
+      End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
+  }
 
   const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
 
diff --git a/llvm/test/Analysis/ScalarEvolution/pr46939-trip-count-count-down.ll b/llvm/test/Analysis/ScalarEvolution/pr46939-trip-count-count-down.ll
--- a/llvm/test/Analysis/ScalarEvolution/pr46939-trip-count-count-down.ll
+++ b/llvm/test/Analysis/ScalarEvolution/pr46939-trip-count-count-down.ll
@@ -6,13 +6,13 @@
 ; CHECK-LABEL: 'reverse_loop'
 ; CHECK-NEXT:  Classifying expressions for: @reverse_loop
 ; CHECK-NEXT:    %i.011 = phi i32 [ %n, %for.body.lr.ph ], [ %dec, %for.body ]
-; CHECK-NEXT:    --> {%n,+,-1}<nsw><%for.body> U: full-set S: full-set Exits: (0 smin %n) LoopDispositions: { %for.body: Computable }
+; CHECK-NEXT:    --> {%n,+,-1}<nsw><%for.body> U: full-set S: full-set Exits: 0 LoopDispositions: { %for.body: Computable }
 ; CHECK-NEXT:    %dec = add nsw i32 %i.011, -1
-; CHECK-NEXT:    --> {(-1 + %n),+,-1}<nw><%for.body> U: full-set S: full-set Exits: (-1 + (0 smin %n)) LoopDispositions: { %for.body: Computable }
+; CHECK-NEXT:    --> {(-1 + %n),+,-1}<nw><%for.body> U: full-set S: full-set Exits: -1 LoopDispositions: { %for.body: Computable }
 ; CHECK-NEXT:  Determining loop execution counts for: @reverse_loop
-; CHECK-NEXT:  Loop %for.body: backedge-taken count is ((-1 * (0 smin %n)) + %n)
+; CHECK-NEXT:  Loop %for.body: backedge-taken count is %n
 ; CHECK-NEXT:  Loop %for.body: max backedge-taken count is 2147483647
-; CHECK-NEXT:  Loop %for.body: Predicated backedge-taken count is ((-1 * (0 smin %n)) + %n)
+; CHECK-NEXT:  Loop %for.body: Predicated backedge-taken count is %n
 ; CHECK-NEXT:   Predicates:
 ; CHECK:       Loop %for.body: Trip multiple is 1
 ;
diff --git a/llvm/test/Transforms/HardwareLoops/scalar-while.ll b/llvm/test/Transforms/HardwareLoops/scalar-while.ll
--- a/llvm/test/Transforms/HardwareLoops/scalar-while.ll
+++ b/llvm/test/Transforms/HardwareLoops/scalar-while.ll
@@ -76,18 +76,14 @@
 ; CHECK-GUARD:   br i1 %cmp4, label %while.end, label %while.body.preheader
 ; CHECK-GUARD: while.body.preheader:
 ; CHECK-GUARD:   [[ADD:%[^ ]+]] = add i32 %i, 1
-; CHECK-GUARD:   [[SEL:%[^ ]+]] = icmp slt i32 %N, %i
-; CHECK-GUARD:   [[MIN:%[^ ]+]] = select i1 [[SEL]], i32 %N, i32 %i
-; CHECK-GUARD:   [[COUNT:%[^ ]+]] = sub i32 [[ADD]], [[MIN]]
+; CHECK-GUARD:   [[COUNT:%[^ ]+]] = sub i32 [[ADD]], %N
 ; CHECK-GUARD:   call void @llvm.set.loop.iterations.i32(i32 [[COUNT]])
 ; CHECK-GUARD:   br label %while.body
 
 ; CHECK-LABEL: while_gte
 ; CHECK: while.body.preheader:
 ; CHECK: [[ADD:%[^ ]+]] = add i32 %i, 1
-; CHECK: [[SEL:%[^ ]+]] = icmp slt i32 %N, %i
-; CHECK: [[MIN:%[^ ]+]] = select i1 [[SEL]], i32 %N, i32 %i
-; CHECK: [[COUNT:%[^ ]+]] = sub i32 [[ADD]], [[MIN]]
+; CHECK: [[COUNT:%[^ ]+]] = sub i32 [[ADD]], %N
 ; CHECK: call void @llvm.set.loop.iterations.i32(i32 [[COUNT]])
 ; CHECK: br label %while.body