diff --git a/pkg/network/discovery.go b/pkg/network/discovery.go
index 221db32ee..cb4e32555 100644
--- a/pkg/network/discovery.go
+++ b/pkg/network/discovery.go
@@ -19,6 +19,7 @@ const (
 type Discoverer interface {
 	BackFill(...string)
 	GetFanOut() int
+	NetworkSize() int
 	PoolCount() int
 	RequestRemote(int)
 	RegisterBadAddr(string)
@@ -48,6 +49,7 @@ type DefaultDiscovery struct {
 	unconnectedAddrs map[string]int
 	attempted        map[string]bool
 	optimalFanOut    int32
+	networkSize      int32
 	requestCh        chan int
 }
 
@@ -233,6 +235,11 @@ func (d *DefaultDiscovery) GetFanOut() int {
 	return int(atomic.LoadInt32(&d.optimalFanOut))
 }
 
+// NetworkSize returns the estimated network size.
+func (d *DefaultDiscovery) NetworkSize() int {
+	return int(atomic.LoadInt32(&d.networkSize))
+}
+
 // updateNetSize updates network size estimation metric. Must be called under read lock.
 func (d *DefaultDiscovery) updateNetSize() {
 	var netsize = len(d.connectedAddrs) + len(d.unconnectedAddrs) + 1 // 1 for the node itself.
@@ -242,6 +249,7 @@ func (d *DefaultDiscovery) updateNetSize() {
 	}
 
 	atomic.StoreInt32(&d.optimalFanOut, int32(fanOut+0.5)) // Truncating conversion, hence +0.5.
+	atomic.StoreInt32(&d.networkSize, int32(netsize))
 	updateNetworkSizeMetric(netsize)
 	updatePoolCountMetric(d.poolCount())
 }
diff --git a/pkg/network/helper_test.go b/pkg/network/helper_test.go
index 5692482cf..00c83a7d0 100644
--- a/pkg/network/helper_test.go
+++ b/pkg/network/helper_test.go
@@ -40,6 +40,11 @@ func (d *testDiscovery) RegisterBadAddr(addr string) {
 	d.bad = append(d.bad, addr)
 }
 func (d *testDiscovery) GetFanOut() int {
+	d.Lock()
+	defer d.Unlock()
+	return (len(d.connected) + len(d.backfill)) * 2 / 3
+}
+func (d *testDiscovery) NetworkSize() int {
 	d.Lock()
 	defer d.Unlock()
 	return len(d.connected) + len(d.backfill)
diff --git a/pkg/network/server.go b/pkg/network/server.go
index 6cef30e0c..888bc44b4 100644
--- a/pkg/network/server.go
+++ b/pkg/network/server.go
@@ -387,10 +387,28 @@ func (s *Server) ConnectedPeers() []string {
 // while itself dealing with peers management (handling connects/disconnects).
 func (s *Server) run() {
 	go s.runProto()
-	for {
-		if s.PeerCount() < s.MinPeers {
+	for loopCnt := 0; ; loopCnt++ {
+		var (
+			netSize = s.discovery.NetworkSize()
+			// "Optimal" number of peers.
+			optimalN = s.discovery.GetFanOut() * 2
+			// Real number of peers.
+			peerN = s.PeerCount()
+		)
+
+		if peerN < s.MinPeers {
+			// Starting up or going below the minimum -> quickly get many new peers.
 			s.discovery.RequestRemote(s.AttemptConnPeers)
+		} else if s.MinPeers > 0 && loopCnt%s.MinPeers == 0 && optimalN > peerN && optimalN < s.MaxPeers && optimalN < netSize {
+			// Having some number of peers, but probably can get some more, the network is big.
+			// It also allows to start picking up new peers proactively, before we suddenly have <s.MinPeers of them.
+			var connN = s.AttemptConnPeers
+			if connN > optimalN-peerN {
+				connN = optimalN - peerN
+			}
+			s.discovery.RequestRemote(connN)
 		}
+
 		if s.discovery.PoolCount() < minPoolCount {
 			s.broadcastHPMessage(NewMessage(CMDGetAddr, payload.NewNullPayload()))
 		}