diff --git a/llvm/lib/Transforms/Vectorize/LoopVectorize.cpp b/llvm/lib/Transforms/Vectorize/LoopVectorize.cpp
--- a/llvm/lib/Transforms/Vectorize/LoopVectorize.cpp
+++ b/llvm/lib/Transforms/Vectorize/LoopVectorize.cpp
@@ -5003,6 +5003,7 @@
   }
 
   unsigned MaxVF = UserVF ? UserVF : computeFeasibleMaxVF(TC);
+  assert((UserVF || isPowerOf2_32(MaxVF)) && "MaxVF must be a power of 2");
   unsigned MaxVFtimesIC = UserIC ? MaxVF * UserIC : MaxVF;
   if (TC > 0 && TC % MaxVFtimesIC == 0) {
     // Accept MaxVF if we do not have a tail.
@@ -5051,6 +5052,9 @@
 
   WidestRegister = std::min(WidestRegister, MaxSafeRegisterWidth);
 
+  // Ensure MaxVF is a power of 2; the dependence distance bound may not be.
+  WidestRegister = PowerOf2Floor(WidestRegister);
+
   unsigned MaxVectorSize = WidestRegister / WidestType;
 
   LLVM_DEBUG(dbgs() << "LV: The Smallest and Widest types: " << SmallestType
diff --git a/llvm/test/Transforms/LoopVectorize/memdep-fold-tail.ll b/llvm/test/Transforms/LoopVectorize/memdep-fold-tail.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/LoopVectorize/memdep-fold-tail.ll
@@ -0,0 +1,108 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt < %s -loop-vectorize -vectorize-num-stores-pred=2 -prefer-predicate-over-epilog -S | FileCheck %s
+
+target datalayout = "e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128-n8:16:32:64-S128"
+
+; Vectorization with dependence checks.
+
+; Check that a non-power-of-2 MaxVF, calculated based on maximum safe distance,
+; does not lead fold-tail to think that no tail will be generated for any chosen
+; (power of 2) VF.
+; Dependence distance here is 3 iterations.
+; Tiny trip count of 15 divides 3, but any (even) VF will have a tail.
+
+;unsigned char a [15+3];
+;void maxvf3(){
+;  for (int j = 0; j < 15; ++j) {
+;    a[j] = 69;
+;    a[j+3] = 7;
+;  }
+;}
+
+@a = common local_unnamed_addr global [18 x i8] zeroinitializer, align 16
+
+define void @maxvf3() {
+; CHECK-LABEL: @maxvf3(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br i1 false, label [[SCALAR_PH:%.*]], label [[VECTOR_PH:%.*]]
+; CHECK:       vector.ph:
+; CHECK-NEXT:    br label [[VECTOR_BODY:%.*]]
+; CHECK:       vector.body:
+; CHECK-NEXT:    [[INDEX:%.*]] = phi i32 [ 0, [[VECTOR_PH]] ], [ [[INDEX_NEXT:%.*]], [[PRED_STORE_CONTINUE6:%.*]] ]
+; CHECK-NEXT:    [[VEC_IND:%.*]] = phi <2 x i32> [ <i32 0, i32 1>, [[VECTOR_PH]] ], [ [[VEC_IND_NEXT:%.*]], [[PRED_STORE_CONTINUE6]] ]
+; CHECK-NEXT:    [[TMP0:%.*]] = icmp ule <2 x i32> [[VEC_IND]], <i32 14, i32 14>
+; CHECK-NEXT:    [[TMP1:%.*]] = extractelement <2 x i1> [[TMP0]], i32 0
+; CHECK-NEXT:    br i1 [[TMP1]], label [[PRED_STORE_IF:%.*]], label [[PRED_STORE_CONTINUE:%.*]]
+; CHECK:       pred.store.if:
+; CHECK-NEXT:    [[TMP2:%.*]] = add i32 [[INDEX]], 0
+; CHECK-NEXT:    [[TMP3:%.*]] = getelementptr inbounds [18 x i8], [18 x i8]* @a, i32 0, i32 [[TMP2]]
+; CHECK-NEXT:    store i8 69, i8* [[TMP3]], align 8
+; CHECK-NEXT:    br label [[PRED_STORE_CONTINUE]]
+; CHECK:       pred.store.continue:
+; CHECK-NEXT:    [[TMP4:%.*]] = extractelement <2 x i1> [[TMP0]], i32 1
+; CHECK-NEXT:    br i1 [[TMP4]], label [[PRED_STORE_IF1:%.*]], label [[PRED_STORE_CONTINUE2:%.*]]
+; CHECK:       pred.store.if1:
+; CHECK-NEXT:    [[TMP5:%.*]] = add i32 [[INDEX]], 1
+; CHECK-NEXT:    [[TMP6:%.*]] = getelementptr inbounds [18 x i8], [18 x i8]* @a, i32 0, i32 [[TMP5]]
+; CHECK-NEXT:    store i8 69, i8* [[TMP6]], align 8
+; CHECK-NEXT:    br label [[PRED_STORE_CONTINUE2]]
+; CHECK:       pred.store.continue2:
+; CHECK-NEXT:    [[TMP7:%.*]] = add nuw nsw <2 x i32> <i32 3, i32 3>, [[VEC_IND]]
+; CHECK-NEXT:    [[TMP8:%.*]] = extractelement <2 x i1> [[TMP0]], i32 0
+; CHECK-NEXT:    br i1 [[TMP8]], label [[PRED_STORE_IF3:%.*]], label [[PRED_STORE_CONTINUE4:%.*]]
+; CHECK:       pred.store.if3:
+; CHECK-NEXT:    [[TMP9:%.*]] = extractelement <2 x i32> [[TMP7]], i32 0
+; CHECK-NEXT:    [[TMP10:%.*]] = getelementptr inbounds [18 x i8], [18 x i8]* @a, i32 0, i32 [[TMP9]]
+; CHECK-NEXT:    store i8 7, i8* [[TMP10]], align 8
+; CHECK-NEXT:    br label [[PRED_STORE_CONTINUE4]]
+; CHECK:       pred.store.continue4:
+; CHECK-NEXT:    [[TMP11:%.*]] = extractelement <2 x i1> [[TMP0]], i32 1
+; CHECK-NEXT:    br i1 [[TMP11]], label [[PRED_STORE_IF5:%.*]], label [[PRED_STORE_CONTINUE6]]
+; CHECK:       pred.store.if5:
+; CHECK-NEXT:    [[TMP12:%.*]] = extractelement <2 x i32> [[TMP7]], i32 1
+; CHECK-NEXT:    [[TMP13:%.*]] = getelementptr inbounds [18 x i8], [18 x i8]* @a, i32 0, i32 [[TMP12]]
+; CHECK-NEXT:    store i8 7, i8* [[TMP13]], align 8
+; CHECK-NEXT:    br label [[PRED_STORE_CONTINUE6]]
+; CHECK:       pred.store.continue6:
+; CHECK-NEXT:    [[INDEX_NEXT]] = add i32 [[INDEX]], 2
+; CHECK-NEXT:    [[VEC_IND_NEXT]] = add <2 x i32> [[VEC_IND]], <i32 2, i32 2>
+; CHECK-NEXT:    [[TMP14:%.*]] = icmp eq i32 [[INDEX_NEXT]], 16
+; CHECK-NEXT:    br i1 [[TMP14]], label [[MIDDLE_BLOCK:%.*]], label [[VECTOR_BODY]], !llvm.loop !0
+; CHECK:       middle.block:
+; CHECK-NEXT:    br i1 true, label [[FOR_END:%.*]], label [[SCALAR_PH]]
+; CHECK:       scalar.ph:
+; CHECK-NEXT:    [[BC_RESUME_VAL:%.*]] = phi i32 [ 16, [[MIDDLE_BLOCK]] ], [ 0, [[ENTRY:%.*]] ]
+; CHECK-NEXT:    br label [[FOR_BODY:%.*]]
+; CHECK:       for.body:
+; CHECK-NEXT:    [[J:%.*]] = phi i32 [ [[BC_RESUME_VAL]], [[SCALAR_PH]] ], [ [[J_NEXT:%.*]], [[FOR_BODY]] ]
+; CHECK-NEXT:    [[AJ:%.*]] = getelementptr inbounds [18 x i8], [18 x i8]* @a, i32 0, i32 [[J]]
+; CHECK-NEXT:    store i8 69, i8* [[AJ]], align 8
+; CHECK-NEXT:    [[JP3:%.*]] = add nuw nsw i32 3, [[J]]
+; CHECK-NEXT:    [[AJP3:%.*]] = getelementptr inbounds [18 x i8], [18 x i8]* @a, i32 0, i32 [[JP3]]
+; CHECK-NEXT:    store i8 7, i8* [[AJP3]], align 8
+; CHECK-NEXT:    [[J_NEXT]] = add nuw nsw i32 [[J]], 1
+; CHECK-NEXT:    [[EXITCOND:%.*]] = icmp eq i32 [[J_NEXT]], 15
+; CHECK-NEXT:    br i1 [[EXITCOND]], label [[FOR_END]], label [[FOR_BODY]], !llvm.loop !2
+; CHECK:       for.end:
+; CHECK-NEXT:    ret void
+;
+entry:
+  br label %for.body
+
+for.body:
+  %j = phi i32 [ 0, %entry ], [ %j.next, %for.body ]
+  %aj = getelementptr inbounds [18 x i8], [18 x i8]* @a, i32 0, i32 %j
+  store i8 69, i8* %aj, align 8
+  %jp3 = add nuw nsw i32 3, %j
+  %ajp3 = getelementptr inbounds [18 x i8], [18 x i8]* @a, i32 0, i32 %jp3
+  store i8 7, i8* %ajp3, align 8
+  %j.next = add nuw nsw i32 %j, 1
+  %exitcond = icmp eq i32 %j.next, 15
+  br i1 %exitcond, label %for.end, label %for.body, !llvm.loop !0
+
+for.end:
+  ret void
+}
+
+!0 = distinct !{!0, !1}
+!1 = !{!"llvm.loop.vectorize.enable", i1 true}