diff --git a/pkg/network/helper_test.go b/pkg/network/helper_test.go
index 9b52a2d91..716ba2afa 100644
--- a/pkg/network/helper_test.go
+++ b/pkg/network/helper_test.go
@@ -415,18 +415,18 @@ func (p *localPeer) EnqueueMessage(msg *Message) error {
 	if err != nil {
 		return err
 	}
-	return p.EnqueuePacket(b)
+	return p.EnqueuePacket(true, b)
 }
-func (p *localPeer) EnqueuePacket(m []byte) error {
-	return p.EnqueueHPPacket(m)
+func (p *localPeer) EnqueuePacket(block bool, m []byte) error {
+	return p.EnqueueHPPacket(block, m)
 }
 func (p *localPeer) EnqueueP2PMessage(msg *Message) error {
 	return p.EnqueueMessage(msg)
 }
 func (p *localPeer) EnqueueP2PPacket(m []byte) error {
-	return p.EnqueueHPPacket(m)
+	return p.EnqueueHPPacket(true, m)
 }
-func (p *localPeer) EnqueueHPPacket(m []byte) error {
+func (p *localPeer) EnqueueHPPacket(_ bool, m []byte) error {
 	msg := &Message{Network: netmode.UnitTestNet}
 	r := io.NewBinReaderFromBuf(m)
 	err := msg.Decode(r)
diff --git a/pkg/network/peer.go b/pkg/network/peer.go
index fb06c59d2..b2df6ff69 100644
--- a/pkg/network/peer.go
+++ b/pkg/network/peer.go
@@ -28,7 +28,7 @@ type Peer interface {
 	// can be shared with other queues (so that message marshalling can be
 	// done once for all peers). Does nothing is the peer is not yet
 	// completed handshaking.
-	EnqueuePacket([]byte) error
+	EnqueuePacket(bool, []byte) error
 
 	// EnqueueP2PMessage is a temporary wrapper that sends a message via
 	// EnqueueP2PPacket if there is no error in serializing it.
@@ -47,7 +47,7 @@ type Peer interface {
 	// EnqueueHPPacket is a blocking high priority packet enqueuer, it
 	// doesn't return until it puts given packet into the high-priority
 	// queue.
-	EnqueueHPPacket([]byte) error
+	EnqueueHPPacket(bool, []byte) error
 	Version() *payload.Version
 	LastBlockIndex() uint32
 	Handshaked() bool
diff --git a/pkg/network/server.go b/pkg/network/server.go
index 8beeea9d2..e4721f1e0 100644
--- a/pkg/network/server.go
+++ b/pkg/network/server.go
@@ -537,7 +537,7 @@ func (s *Server) handleInvCmd(p Peer, inv *payload.Inventory) error {
 			return err
 		}
 		if inv.Type == payload.ConsensusType {
-			return p.EnqueueHPPacket(pkt)
+			return p.EnqueueHPPacket(true, pkt)
 		}
 		return p.EnqueueP2PPacket(pkt)
 	}
@@ -599,7 +599,7 @@ func (s *Server) handleGetDataCmd(p Peer, inv *payload.Inventory) error {
 			pkt, err := msg.Bytes()
 			if err == nil {
 				if inv.Type == payload.ConsensusType {
-					err = p.EnqueueHPPacket(pkt)
+					err = p.EnqueueHPPacket(true, pkt)
 				} else {
 					err = p.EnqueueP2PPacket(pkt)
 				}
@@ -943,7 +943,7 @@ func (s *Server) requestTx(hashes ...util.Uint256) {
 // iteratePeersWithSendMsg sends given message to all peers using two functions
 // passed, one is to send the message and the other is to filtrate peers (the
 // peer is considered invalid if it returns false).
-func (s *Server) iteratePeersWithSendMsg(msg *Message, send func(Peer, []byte) error, peerOK func(Peer) bool) {
+func (s *Server) iteratePeersWithSendMsg(msg *Message, send func(Peer, bool, []byte) error, peerOK func(Peer) bool) {
 	// Get a copy of s.peers to avoid holding a lock while sending.
 	peers := s.Peers()
 	if len(peers) == 0 {
@@ -953,15 +953,46 @@ func (s *Server) iteratePeersWithSendMsg(msg *Message, send func(Peer, []byte) e
 	if err != nil {
 		return
 	}
+
+	success := make(map[Peer]bool, len(peers))
+	okCount := 0
+	sentCount := 0
 	for peer := range peers {
 		if peerOK != nil && !peerOK(peer) {
+			success[peer] = false
+			continue
+		}
+		okCount++
+		if err := send(peer, false, pkt); err != nil {
 			continue
 		}
 		if msg.Command == CMDGetAddr {
 			peer.AddGetAddrSent()
 		}
-		// Who cares about these messages anyway?
-		_ = send(peer, pkt)
+		success[peer] = true
+		sentCount++
+	}
+
+	// Send to at least 2/3 of good peers.
+	if 3*sentCount >= 2*okCount {
+		return
+	}
+
+	// Perform blocking send now.
+	for peer := range peers {
+		if _, ok := success[peer]; ok || peerOK != nil && !peerOK(peer) {
+			continue
+		}
+		if err := send(peer, true, pkt); err != nil {
+			continue
+		}
+		if msg.Command == CMDGetAddr {
+			peer.AddGetAddrSent()
+		}
+		sentCount++
+		if 3*sentCount >= 2*okCount {
+			return
+		}
 	}
 }
 
diff --git a/pkg/network/tcp_peer.go b/pkg/network/tcp_peer.go
index 67329c161..f55a3954b 100644
--- a/pkg/network/tcp_peer.go
+++ b/pkg/network/tcp_peer.go
@@ -30,6 +30,7 @@ const (
 
 var (
 	errGone           = errors.New("the peer is gone already")
+	errBusy           = errors.New("peer is busy")
 	errStateMismatch  = errors.New("tried to send protocol message before handshake completed")
 	errPingPong       = errors.New("ping/pong timeout")
 	errUnexpectedPong = errors.New("pong message wasn't expected")
@@ -81,21 +82,31 @@ func NewTCPPeer(conn net.Conn, s *Server) *TCPPeer {
 
 // putPacketIntoQueue puts given message into the given queue if the peer has
 // done handshaking.
-func (p *TCPPeer) putPacketIntoQueue(queue chan<- []byte, msg []byte) error {
+func (p *TCPPeer) putPacketIntoQueue(queue chan<- []byte, block bool, msg []byte) error {
 	if !p.Handshaked() {
 		return errStateMismatch
 	}
-	select {
-	case queue <- msg:
-	case <-p.done:
-		return errGone
+	if block {
+		select {
+		case queue <- msg:
+		case <-p.done:
+			return errGone
+		}
+	} else {
+		select {
+		case queue <- msg:
+		case <-p.done:
+			return errGone
+		default:
+			return errBusy
+		}
 	}
 	return nil
 }
 
 // EnqueuePacket implements the Peer interface.
-func (p *TCPPeer) EnqueuePacket(msg []byte) error {
-	return p.putPacketIntoQueue(p.sendQ, msg)
+func (p *TCPPeer) EnqueuePacket(block bool, msg []byte) error {
+	return p.putPacketIntoQueue(p.sendQ, block, msg)
 }
 
 // putMessageIntoQueue serializes given Message and puts it into given queue if
@@ -105,7 +116,7 @@ func (p *TCPPeer) putMsgIntoQueue(queue chan<- []byte, msg *Message) error {
 	if err != nil {
 		return err
 	}
-	return p.putPacketIntoQueue(queue, b)
+	return p.putPacketIntoQueue(queue, true, b)
 }
 
 // EnqueueMessage is a temporary wrapper that sends a message via
@@ -116,7 +127,7 @@ func (p *TCPPeer) EnqueueMessage(msg *Message) error {
 
 // EnqueueP2PPacket implements the Peer interface.
 func (p *TCPPeer) EnqueueP2PPacket(msg []byte) error {
-	return p.putPacketIntoQueue(p.p2pSendQ, msg)
+	return p.putPacketIntoQueue(p.p2pSendQ, true, msg)
 }
 
 // EnqueueP2PMessage implements the Peer interface.
@@ -126,8 +137,8 @@ func (p *TCPPeer) EnqueueP2PMessage(msg *Message) error {
 
 // EnqueueHPPacket implements the Peer interface. It the peer is not yet
 // handshaked it's a noop.
-func (p *TCPPeer) EnqueueHPPacket(msg []byte) error {
-	return p.putPacketIntoQueue(p.hpSendQ, msg)
+func (p *TCPPeer) EnqueueHPPacket(block bool, msg []byte) error {
+	return p.putPacketIntoQueue(p.hpSendQ, block, msg)
 }
 
 func (p *TCPPeer) writeMsg(msg *Message) error {