diff --git a/federationsender/queue/destinationqueue.go b/federationsender/queue/destinationqueue.go
index 7ab6f1f16..a574950cd 100644
--- a/federationsender/queue/destinationqueue.go
+++ b/federationsender/queue/destinationqueue.go
@@ -22,6 +22,7 @@ import (
 
 	"github.com/matrix-org/dendrite/federationsender/producers"
 	"github.com/matrix-org/dendrite/federationsender/types"
+	"github.com/matrix-org/gomatrix"
 	"github.com/matrix-org/gomatrixserverlib"
 	"github.com/sirupsen/logrus"
 	log "github.com/sirupsen/logrus"
@@ -102,11 +103,26 @@ func (oq *destinationQueue) backgroundSend() {
 		// idle timeout.
 		select {
 		case pdu := <-oq.incomingPDUs:
+			// Ordering of PDUs is important so we add them to the end
+			// of the queue and they will all be added to transactions
+			// in order.
 			oq.pendingPDUs = append(oq.pendingPDUs, pdu)
 		case edu := <-oq.incomingEDUs:
+			// Likewise for EDUs, although we should probably not try
+			// too hard with some EDUs (like typing notifications) after
+			// a certain amount of time has passed.
+			// TODO: think about EDU expiry some more
 			oq.pendingEDUs = append(oq.pendingEDUs, edu)
 		case invite := <-oq.incomingInvites:
-			oq.pendingInvites = append(oq.pendingInvites, invite)
+			// There's no strict ordering requirement for invites like
+			// there is for transactions, so we put the invite onto the
+			// front of the queue. This means that if an invite that is
+			// stuck failing already, that it won't block our new invite
+			// from being sent.
+			oq.pendingInvites = append(
+				[]*gomatrixserverlib.InviteV2Request{invite},
+				oq.pendingInvites...,
+			)
 		case <-time.After(time.Second * 30):
 			// The worker is idle so stop the goroutine. It'll
 			// get restarted automatically the next time we
@@ -221,16 +237,33 @@ func (oq *destinationQueue) nextTransaction(
 
 	logrus.WithField("server_name", oq.destination).Infof("Sending transaction %q containing %d PDUs, %d EDUs", t.TransactionID, len(t.PDUs), len(t.EDUs))
 
+	// TODO: we should check for 500-ish fails vs 400-ish here,
+	// since we shouldn't queue things indefinitely in response
+	// to a 400-ish error
 	_, err := oq.client.SendTransaction(context.TODO(), t)
-	if err != nil {
+	switch e := err.(type) {
+	case nil:
+		// No error was returned so the transaction looks to have
+		// been successfully sent.
+		return true, nil
+	case gomatrix.HTTPError:
+		// We received a HTTP error back. In this instance we only
+		// should report an error if
+		if e.Code >= 400 && e.Code <= 499 {
+			// We tried but the remote side has sent back a client error.
+			// It's no use retrying because it will happen again.
+			return true, nil
+		}
+		// Otherwise, report that we failed to send the transaction
+		// and we will retry again.
+		return false, err
+	default:
 		log.WithFields(log.Fields{
 			"destination": oq.destination,
 			log.ErrorKey:  err,
 		}).Info("problem sending transaction")
 		return false, err
 	}
-
-	return true, nil
 }
 
 // nextInvite takes pending invite events from the queue and sends
@@ -253,7 +286,26 @@ func (oq *destinationQueue) nextInvites(
 			oq.destination,
 			*inviteReq,
 		)
-		if err != nil {
+		switch e := err.(type) {
+		case nil:
+			done++
+		case gomatrix.HTTPError:
+			log.WithFields(log.Fields{
+				"event_id":    ev.EventID(),
+				"state_key":   ev.StateKey(),
+				"destination": oq.destination,
+				"status_code": e.Code,
+			}).WithError(err).Error("failed to send invite due to HTTP error")
+			// Check whether we should do something about the error or
+			// just accept it as unavoidable.
+			if e.Code >= 400 && e.Code <= 499 {
+				// We tried but the remote side has sent back a client error.
+				// It's no use retrying because it will happen again.
+				done++
+				continue
+			}
+			return done, err
+		default:
 			log.WithFields(log.Fields{
 				"event_id":    ev.EventID(),
 				"state_key":   ev.StateKey(),
@@ -274,8 +326,6 @@ func (oq *destinationQueue) nextInvites(
 			}).WithError(err).Error("failed to return signed invite to roomserver")
 			return done, err
 		}
-
-		done++
 	}
 
 	return done, nil