diff --git a/store/heightsub.go b/store/heightsub.go
index 2335001..002505a 100644
--- a/store/heightsub.go
+++ b/store/heightsub.go
@@ -19,12 +19,14 @@ type heightSub[H header.Header[H]] struct {
 	height       atomic.Uint64
 	heightReqsLk sync.Mutex
 	heightReqs   map[uint64]map[chan H]struct{}
+	knownHeights map[uint64]struct{}
 }
 
 // newHeightSub instantiates new heightSub.
 func newHeightSub[H header.Header[H]]() *heightSub[H] {
 	return &heightSub[H]{
-		heightReqs: make(map[uint64]map[chan H]struct{}),
+		heightReqs:   make(map[uint64]map[chan H]struct{}),
+		knownHeights: map[uint64]struct{}{},
 	}
 }
 
@@ -89,17 +91,13 @@ func (hs *heightSub[H]) Pub(headers ...H) {
 		return
 	}
 
-	height := hs.Height()
 	from, to := headers[0].Height(), headers[ln-1].Height()
-	if height+1 != from && height != 0 { // height != 0 is needed to enable init from any height and not only 1
-		log.Fatalf("PLEASE FILE A BUG REPORT: headers given to the heightSub are in the wrong order: expected %d, got %d", height+1, from)
-		return
-	}
-	hs.SetHeight(to)
 
 	hs.heightReqsLk.Lock()
 	defer hs.heightReqsLk.Unlock()
 
+	hs.tryAdvanceHeight(headers...)
+
 	// there is a common case where we Pub only header
 	// in this case, we shouldn't loop over each heightReqs
 	// and instead read from the map directly
@@ -128,3 +126,26 @@ func (hs *heightSub[H]) Pub(headers ...H) {
 		}
 	}
 }
+
+func (hs *heightSub[H]) tryAdvanceHeight(headers ...H) {
+	curr := hs.Height()
+
+	// collect all new heights.
+	for i := range headers {
+		h := headers[i].Height()
+		if h > curr {
+			hs.knownHeights[h] = struct{}{}
+		}
+	}
+
+	// try advance heightSub.Height if we saw a relevant height before.
+	for len(hs.knownHeights) > 0 {
+		_, ok := hs.knownHeights[curr+1]
+		if !ok {
+			break
+		}
+		delete(hs.knownHeights, curr+1)
+		curr++
+	}
+	hs.SetHeight(curr)
+}
diff --git a/store/heightsub_test.go b/store/heightsub_test.go
index 3a48d95..64ef180 100644
--- a/store/heightsub_test.go
+++ b/store/heightsub_test.go
@@ -47,6 +47,37 @@ func TestHeightSub(t *testing.T) {
 	}
 }
 
+func TestHeightSubNonAdjacement(t *testing.T) {
+	ctx, cancel := context.WithTimeout(context.Background(), time.Second*5)
+	defer cancel()
+
+	hs := newHeightSub[*headertest.DummyHeader]()
+
+	{
+		h := headertest.RandDummyHeader(t)
+		h.HeightI = 100
+		hs.SetHeight(99)
+		hs.Pub(h)
+	}
+
+	{
+		go func() {
+			// fixes flakiness on CI
+			time.Sleep(time.Millisecond)
+
+			h1 := headertest.RandDummyHeader(t)
+			h1.HeightI = 200
+			h2 := headertest.RandDummyHeader(t)
+			h2.HeightI = 300
+			hs.Pub(h1, h2)
+		}()
+
+		h, err := hs.Sub(ctx, 200)
+		assert.NoError(t, err)
+		assert.NotNil(t, h)
+	}
+}
+
 func TestHeightSubCancellation(t *testing.T) {
 	ctx, cancel := context.WithTimeout(context.Background(), time.Second)
 	defer cancel()
diff --git a/store/store_test.go b/store/store_test.go
index 53d40d5..e52ddb6 100644
--- a/store/store_test.go
+++ b/store/store_test.go
@@ -141,6 +141,58 @@ func TestStore_Append_BadHeader(t *testing.T) {
 	require.Error(t, err)
 }
 
+func TestStore_Append_stableHeadWhenGaps(t *testing.T) {
+	ctx, cancel := context.WithTimeout(context.Background(), 5*time.Second)
+	t.Cleanup(cancel)
+
+	suite := headertest.NewTestSuite(t)
+
+	ds := sync.MutexWrap(datastore.NewMapDatastore())
+	store := NewTestStore(t, ctx, ds, suite.Head(), WithWriteBatchSize(4))
+
+	head, err := store.Head(ctx)
+	require.NoError(t, err)
+	assert.Equal(t, head.Hash(), suite.Head().Hash())
+
+	in := suite.GenDummyHeaders(5)
+
+	err = store.Append(ctx, in...)
+	require.NoError(t, err)
+	// wait for batch to be written.
+	time.Sleep(100 * time.Millisecond)
+
+	wantHead := in[4] // last header from incomming headers.
+
+	head, err = store.Head(ctx)
+	require.NoError(t, err)
+	assert.Equal(t, head.Hash(), wantHead.Hash())
+
+	in = suite.GenDummyHeaders(10)
+	// make a gap
+	missedHeaders, in := in[:5], in[5:]
+	latestHead := in[len(in)-1]
+
+	err = store.Append(ctx, in...)
+	require.NoError(t, err)
+	// wait for batch to be written.
+	time.Sleep(100 * time.Millisecond)
+
+	// head is not advanced due to a gap.
+	head, err = store.Head(ctx)
+	require.NoError(t, err)
+	assert.Equal(t, head.Hash(), wantHead.Hash())
+
+	err = store.Append(ctx, missedHeaders...)
+	require.NoError(t, err)
+	// wait for batch to be written.
+	time.Sleep(100 * time.Millisecond)
+
+	// after appending missing headers we're on a latest header.
+	head, err = store.Head(ctx)
+	require.NoError(t, err)
+	assert.Equal(t, head.Hash(), latestHead.Hash())
+}
+
 // TestStore_GetRange tests possible combinations of requests and ensures that
 // the store can handle them adequately (even malformed requests)
 func TestStore_GetRange(t *testing.T) {