diff --git a/eth/handler.go b/eth/handler.go
index 8283d7d02fe2..86e94cada6d1 100644
--- a/eth/handler.go
+++ b/eth/handler.go
@@ -52,6 +52,9 @@ const (
 	// All transactions with a higher size will be announced and need to be fetched
 	// by the peer.
 	txMaxBroadcastSize = 4096
+
+	// Hysteresis to stabilize the number of direct peers to send transactions to.
+	directPeersHysteresis = 0.5
 )
 
 var syncChallengeTimeout = 15 * time.Second // Time allowance for a node to reply to the sync progress challenge
@@ -110,10 +113,11 @@ type handler struct {
 	snapSync atomic.Bool // Flag whether snap sync is enabled (gets disabled if we already have blocks)
 	synced   atomic.Bool // Flag whether we're considered synchronised (enables transaction processing)
 
-	database ethdb.Database
-	txpool   txPool
-	chain    *core.BlockChain
-	maxPeers int
+	database   ethdb.Database
+	txpool     txPool
+	chain      *core.BlockChain
+	maxPeers   int
+	lastDirect atomic.Int64 // Last number of peers we sent transactions to, used to stabilize the randomness
 
 	downloader *downloader.Downloader
 	txFetcher  *fetcher.TxFetcher
@@ -477,11 +481,21 @@ func (h *handler) BroadcastTransactions(txs types.Transactions) {
 		annos = make(map[*ethPeer][]common.Hash) // Set peer->hash to announce
 	)
 	// Broadcast transactions to a batch of peers not knowing about it
-	direct := big.NewInt(int64(math.Sqrt(float64(h.peers.len())))) // Approximate number of peers to broadcast to
-	if direct.BitLen() == 0 {
-		direct = big.NewInt(1)
+	sqrtPeers := math.Sqrt(float64(h.peers.len())) // Approximate number of peers to broadcast to
+
+	// Use some hysteresis to avoid oscillating between two values, stabilising the modulus in the peer selection
+	// If the number of peers is small, use a minimum of 1 peer
+	var directInt int64
+	lastDirect := h.lastDirect.Load()
+	if int64(sqrtPeers) >= lastDirect {
+		directInt = max(int64(sqrtPeers), 1)
+	} else {
+		directInt = max(min(int64(sqrtPeers+directPeersHysteresis), lastDirect), 1)
 	}
-	total := new(big.Int).Exp(direct, big.NewInt(2), nil) // Stabilise total peer count a bit based on sqrt peers
+	h.lastDirect.Store(directInt)
+
+	direct := big.NewInt(directInt)            // Number of peers to send directly to
+	total := big.NewInt(directInt * directInt) // Stabilise total peer count a bit based on sqrt peers
 
 	var (
 		signer = types.LatestSigner(h.chain.Config()) // Don't care about chain status, we just need *a* sender