Index: llvm/lib/Transforms/Scalar/LoopDeletion.cpp
===================================================================
--- llvm/lib/Transforms/Scalar/LoopDeletion.cpp
+++ llvm/lib/Transforms/Scalar/LoopDeletion.cpp
@@ -176,8 +176,10 @@
   const SCEV *S = nullptr;
   // TODO: Once ScalarEvolution supports getValueOnNthIteration for anything
   // else but AddRecs, it's a good use case for it. So far, just consider some
-  // simple cases, like arithmetic operations.
+  // simple cases, like arithmetic operations and selects.
+  ICmpInst::Predicate Pred;
   Value *LHS, *RHS;
+  Value *IfTrue, *IfFalse;
   using namespace PatternMatch;
   if (match(V, m_Add(m_Value(LHS), m_Value(RHS)))) {
     const SCEV *LHSS = getSCEVOnFirstIteration(LHS, L, SE, FirstIterSCEV);
@@ -191,6 +193,17 @@
     const SCEV *LHSS = getSCEVOnFirstIteration(LHS, L, SE, FirstIterSCEV);
     const SCEV *RHSS = getSCEVOnFirstIteration(RHS, L, SE, FirstIterSCEV);
     S = SE.getMulExpr(LHSS, RHSS);
+  } else if (match(V, m_Select(m_ICmp(Pred, m_Value(LHS), m_Value(RHS)),
+                               m_Value(IfTrue), m_Value(IfFalse)))) {
+    const SCEV *LHSS = getSCEVOnFirstIteration(LHS, L, SE, FirstIterSCEV);
+    const SCEV *RHSS = getSCEVOnFirstIteration(RHS, L, SE, FirstIterSCEV);
+    if (SE.isKnownPredicate(Pred, LHSS, RHSS))
+      S = getSCEVOnFirstIteration(IfTrue, L, SE, FirstIterSCEV);
+    else if (SE.isKnownPredicate(ICmpInst::getInversePredicate(Pred), LHSS,
+                                 RHSS))
+      S = getSCEVOnFirstIteration(IfFalse, L, SE, FirstIterSCEV);
+    else
+      S = SE.getSCEV(V);
   } else
     S = SE.getSCEV(V);
   assert(S && "Case not handled?");
Index: llvm/test/Transforms/LoopDeletion/eval_first_iteration.ll
===================================================================
--- llvm/test/Transforms/LoopDeletion/eval_first_iteration.ll
+++ llvm/test/Transforms/LoopDeletion/eval_first_iteration.ll
@@ -781,25 +781,26 @@
   unreachable
 }
 
-; TODO: We can break the backedge here.
 define i32 @test_select_const(i32 %x) {
 ; CHECK-LABEL: @test_select_const(
 ; CHECK-NEXT:  entry:
 ; CHECK-NEXT:    br label [[LOOP:%.*]]
 ; CHECK:       loop:
-; CHECK-NEXT:    [[SUM:%.*]] = phi i32 [ 0, [[ENTRY:%.*]] ], [ [[SUM_NEXT:%.*]], [[BACKEDGE:%.*]] ]
+; CHECK-NEXT:    [[SUM:%.*]] = phi i32 [ 0, [[ENTRY:%.*]] ]
 ; CHECK-NEXT:    [[SUB:%.*]] = sub i32 4, [[SUM]]
 ; CHECK-NEXT:    [[IS_POSITIVE:%.*]] = icmp sgt i32 [[SUB]], 0
 ; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[IS_POSITIVE]], i32 [[SUB]], i32 [[X:%.*]]
 ; CHECK-NEXT:    [[SEL_COND:%.*]] = icmp sgt i32 [[SEL]], 0
-; CHECK-NEXT:    br i1 [[SEL_COND]], label [[BACKEDGE]], label [[IF_FALSE:%.*]]
+; CHECK-NEXT:    br i1 [[SEL_COND]], label [[BACKEDGE:%.*]], label [[IF_FALSE:%.*]]
 ; CHECK:       if.false:
 ; CHECK-NEXT:    br label [[BACKEDGE]]
 ; CHECK:       backedge:
 ; CHECK-NEXT:    [[MERGE_PHI:%.*]] = phi i32 [ 0, [[IF_FALSE]] ], [ [[SUB]], [[LOOP]] ]
-; CHECK-NEXT:    [[SUM_NEXT]] = add i32 [[SUM]], [[MERGE_PHI]]
+; CHECK-NEXT:    [[SUM_NEXT:%.*]] = add i32 [[SUM]], [[MERGE_PHI]]
 ; CHECK-NEXT:    [[LOOP_COND:%.*]] = icmp ne i32 [[SUM_NEXT]], 4
-; CHECK-NEXT:    br i1 [[LOOP_COND]], label [[LOOP]], label [[DONE:%.*]]
+; CHECK-NEXT:    br i1 [[LOOP_COND]], label [[BACKEDGE_LOOP_CRIT_EDGE:%.*]], label [[DONE:%.*]]
+; CHECK:       backedge.loop_crit_edge:
+; CHECK-NEXT:    unreachable
 ; CHECK:       done:
 ; CHECK-NEXT:    [[SUM_NEXT_LCSSA:%.*]] = phi i32 [ [[SUM_NEXT]], [[BACKEDGE]] ]
 ; CHECK-NEXT:    ret i32 [[SUM_NEXT_LCSSA]]