diff --git a/store/heightsub.go b/store/heightsub.go
index 2335001d..80139c74 100644
--- a/store/heightsub.go
+++ b/store/heightsub.go
@@ -34,8 +34,17 @@ func (hs *heightSub[H]) Height() uint64 {
 }
 
 // SetHeight sets the new head height for heightSub.
+// Only the higher height can be set, otherwise no-op.
 func (hs *heightSub[H]) SetHeight(height uint64) {
-	hs.height.Store(height)
+	for {
+		curr := hs.height.Load()
+		if curr > height {
+			return
+		}
+		if hs.height.CompareAndSwap(curr, height) {
+			return
+		}
+	}
 }
 
 // Sub subscribes for a header of a given height.
@@ -89,12 +98,7 @@ 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()
@@ -114,17 +118,17 @@ func (hs *heightSub[H]) Pub(headers ...H) {
 		return
 	}
 
-	// instead of looping over each header in 'headers', we can loop over each request
-	// which will drastically decrease idle iterations, as there will be less requests than headers
-	for height, reqs := range hs.heightReqs {
-		// then we look if any of the requests match the given range of headers
-		if height >= from && height <= to {
-			// and if so, calculate its position and fulfill requests
-			h := headers[height-from]
-			for req := range reqs {
-				req <- h // reqs must always be buffered, so this won't block
-			}
-			delete(hs.heightReqs, height)
+	for _, h := range headers {
+		height := h.Height()
+
+		reqs, ok := hs.heightReqs[height]
+		if !ok {
+			continue
+		}
+
+		for req := range reqs {
+			req <- h // reqs must always be buffered, so this won't block
 		}
+		delete(hs.heightReqs, height)
 	}
 }
diff --git a/store/heightsub_test.go b/store/heightsub_test.go
index 3a48d950..64ef1804 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.go b/store/store.go
index 657a22c7..ef908a9a 100644
--- a/store/store.go
+++ b/store/store.go
@@ -1,9 +1,11 @@
 package store
 
 import (
+	"cmp"
 	"context"
 	"errors"
 	"fmt"
+	"slices"
 	"sync/atomic"
 	"time"
 
@@ -319,6 +321,10 @@ func (s *Store[H]) Append(ctx context.Context, headers ...H) error {
 		head = *headPtr
 	}
 
+	slices.SortFunc(headers, func(a, b H) int {
+		return cmp.Compare(a.Height(), b.Height())
+	})
+
 	// collect valid headers
 	verified := make([]H, 0, lh)
 	for i, h := range headers {