diff --git a/storage/reads/merge.go b/storage/reads/merge.go
index 46930a52db2..b28b92126ba 100644
--- a/storage/reads/merge.go
+++ b/storage/reads/merge.go
@@ -121,49 +121,93 @@ func (h *resultSetHeap) Pop() interface{} {
 	return item
 }
 
+// MergedStringIterator merges multiple storage.StringIterators into one.
+// It sorts and deduplicates adjacent values, so the output is sorted iff all inputs are sorted.
+// If all inputs are not sorted, then output order and deduplication are undefined and unpleasant.
 type MergedStringIterator struct {
-	iterators    []cursors.StringIterator
-	uniqueValues map[string]struct{}
-	nextValue    string
+	heap      stringIteratorHeap
+	nextValue string
 }
 
 // API compatibility
 var _ cursors.StringIterator = (*MergedStringIterator)(nil)
 
 func NewMergedStringIterator(iterators []cursors.StringIterator) *MergedStringIterator {
-	return &MergedStringIterator{
-		iterators:    iterators,
-		uniqueValues: make(map[string]struct{}),
+	nonEmptyIterators := make([]cursors.StringIterator, 0, len(iterators))
+
+	for _, iterator := range iterators {
+		// All iterators must be Next()'d so that their Value() methods return a meaningful value, and sort properly.
+		if iterator.Next() {
+			nonEmptyIterators = append(nonEmptyIterators, iterator)
+		}
+	}
+
+	msi := &MergedStringIterator{
+		heap: stringIteratorHeap{iterators: nonEmptyIterators},
 	}
+	heap.Init(&msi.heap)
+
+	return msi
 }
 
-func (mr *MergedStringIterator) Next() bool {
-	// TODO assume that each iterator is sorted, and iterate in sorted order
-	// https://github.com/influxdata/influxdb/issues/13440
-	for len(mr.iterators) > 0 {
-		iterator := mr.iterators[0]
+func (msi *MergedStringIterator) Next() bool {
+	for msi.heap.Len() > 0 {
+		iterator := msi.heap.iterators[0]
+
+		haveNext := false
+		if proposedNextValue := iterator.Value(); proposedNextValue != msi.nextValue { // Skip dupes.
+			msi.nextValue = proposedNextValue
+			haveNext = true
+		}
 
-		for iterator.Next() {
-			mr.nextValue = iterator.Value()
-			if _, found := mr.uniqueValues[mr.nextValue]; !found {
-				mr.uniqueValues[mr.nextValue] = struct{}{}
-				return true
-			}
+		if iterator.Next() {
+			// iterator.Value() has changed, so re-order that iterator within the heap
+			heap.Fix(&msi.heap, 0)
+		} else {
+			// iterator is drained, so remove it from the heap
+			heap.Pop(&msi.heap)
 		}
 
-		// This iterator exhausted; move on to next iterator.
-		mr.iterators[0] = nil
-		mr.iterators = mr.iterators[1:]
+		if haveNext {
+			return true
+		}
 	}
 
-	mr.uniqueValues = nil
 	return false
 }
 
-func (mr *MergedStringIterator) Value() string {
-	return mr.nextValue
+func (msi *MergedStringIterator) Value() string {
+	return msi.nextValue
 }
 
-func (mr *MergedStringIterator) Stats() cursors.CursorStats {
+func (msi *MergedStringIterator) Stats() cursors.CursorStats {
 	return cursors.CursorStats{}
 }
+
+type stringIteratorHeap struct {
+	iterators []cursors.StringIterator
+}
+
+func (h stringIteratorHeap) Len() int {
+	return len(h.iterators)
+}
+
+func (h stringIteratorHeap) Less(i, j int) bool {
+	return h.iterators[i].Value() < h.iterators[j].Value()
+}
+
+func (h *stringIteratorHeap) Swap(i, j int) {
+	h.iterators[i], h.iterators[j] = h.iterators[j], h.iterators[i]
+}
+
+func (h *stringIteratorHeap) Push(x interface{}) {
+	h.iterators = append(h.iterators, x.(cursors.StringIterator))
+}
+
+func (h *stringIteratorHeap) Pop() interface{} {
+	n := len(h.iterators)
+	item := h.iterators[n-1]
+	h.iterators[n-1] = nil
+	h.iterators = h.iterators[:n-1]
+	return item
+}
diff --git a/storage/reads/merge_test.go b/storage/reads/merge_test.go
index e3685912aff..fddc70e0541 100644
--- a/storage/reads/merge_test.go
+++ b/storage/reads/merge_test.go
@@ -115,19 +115,20 @@ func TestNewMergedStringIterator(t *testing.T) {
 		{
 			name: "simple",
 			iterators: []cursors.StringIterator{
-				newMockStringIterator("foo", "bar"),
+				newMockStringIterator("bar", "foo"),
 			},
-			expectedValues: []string{"foo", "bar"},
+			expectedValues: []string{"bar", "foo"},
 		},
 		{
 			name: "duplicates",
 			iterators: []cursors.StringIterator{
-				newMockStringIterator("foo"),
-				newMockStringIterator("bar", "bar"),
-				newMockStringIterator("foo"),
-				newMockStringIterator("baz", "qux"),
+				newMockStringIterator("c"),
+				newMockStringIterator("b", "b"), // This kind of duplication is not explicitly documented, but works.
+				newMockStringIterator("a", "c"),
+				newMockStringIterator("b", "d"),
+				newMockStringIterator("0", "a", "b", "e"),
 			},
-			expectedValues: []string{"foo", "bar", "baz", "qux"},
+			expectedValues: []string{"0", "a", "b", "c", "d", "e"},
 		},
 	}