Index: lib/Analysis/MustExecute.cpp
===================================================================
--- lib/Analysis/MustExecute.cpp
+++ lib/Analysis/MustExecute.cpp
@@ -70,6 +70,11 @@
   auto *BI = dyn_cast<BranchInst>(CondExitBlock->getTerminator());
   if (!BI || !BI->isConditional())
     return false;
+  // If condition is constant and false leads to ExitBlock then we always
+  // execute the true branch.
+  if (auto *Cond = dyn_cast<ConstantInt>(BI->getCondition()))
+    if (BI->getSuccessor(Cond->getZExtValue() ? 1 : 0) == ExitBlock)
+      return true;
   auto *Cond = dyn_cast<CmpInst>(BI->getCondition());
   if (!Cond)
     return false;
Index: test/Analysis/MustExecute/const-cond.ll
===================================================================
--- /dev/null
+++ test/Analysis/MustExecute/const-cond.ll
@@ -0,0 +1,44 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -disable-output -print-mustexecute %s 2>&1 | FileCheck %s
+
+define i1 @const_cond(i32 %high) {
+; CHECK-LABEL: @const_cond(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br label [[LOOP:%.*]]
+; CHECK:       loop:
+; CHECK-NEXT:    [[IV:%.*]] = phi i32 [ 0, [[ENTRY:%.*]] ], [ [[IV_NEXT:%.*]], [[BACKEDGE:%.*]] ] ; (mustexec in: loop)
+; CHECK-NEXT:    br i1 true, label [[NEXT:%.*]], label [[NEVER1:%.*]] ; (mustexec in: loop)
+; CHECK:       next:
+; CHECK-NEXT:    br i1 false, label [[NEVER2:%.*]], label [[BACKEDGE]] ; (mustexec in: loop)
+; CHECK:       backedge:
+; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i32 [[IV]], 1 ; (mustexec in: loop)
+; CHECK-NEXT:    [[EXIT_TEST:%.*]] = icmp slt i32 [[IV]], [[HIGH:%.*]] ; (mustexec in: loop)
+; CHECK-NEXT:    br i1 [[EXIT_TEST]], label [[LOOP]], label [[EXIT:%.*]] ; (mustexec in: loop)
+; CHECK:       exit:
+; CHECK-NEXT:    ret i1 false
+; CHECK:       never1:
+; CHECK-NEXT:    unreachable
+; CHECK:       never2:
+; CHECK-NEXT:    unreachable
+;
+entry:
+  br label %loop
+
+loop:
+  %iv = phi i32 [0, %entry], [%iv.next, %backedge]
+  br i1 true, label %next, label %never1
+next:
+  br i1 false, label %never2, label %backedge
+backedge:
+  %iv.next = add nsw nuw i32 %iv, 1
+  %exit.test = icmp slt i32 %iv, %high
+  br i1 %exit.test, label %loop, label %exit
+
+exit:
+  ret i1 false
+never1:
+  unreachable
+never2:
+  unreachable
+}
+
Index: test/Transforms/LICM/hoist-mustexec.ll
===================================================================
--- test/Transforms/LICM/hoist-mustexec.ll
+++ test/Transforms/LICM/hoist-mustexec.ll
@@ -218,6 +218,9 @@
 define i32 @test-wrongphi(i32* noalias nocapture readonly %a) nounwind uwtable {
 ; CHECK-LABEL: @test-wrongphi(
 entry:
+; CHECK-LABEL: entry
+; CHECK: %i1 = load i32, i32* %a, align 4
+; CHECK-NEXT: br label %for.body
   br label %for.body
   
 for.body:
@@ -230,7 +233,7 @@
   br i1 %r.chk, label %fail, label %continue
 continue:
 ; CHECK-LABEL: continue
-; CHECK: %i1 = load i32, i32* %a, align 4
+; CHECK-NOT: %i1 = load i32, i32* %a, align 4
   %i1 = load i32, i32* %a, align 4
   %add = add nsw i32 %i1, %acc
   %inc = add nuw nsw i32 %iv, 1