diff --git a/p2p/net/connmgr/connmgr.go b/p2p/net/connmgr/connmgr.go
index 22b83c44eb..c3587ad4e3 100644
--- a/p2p/net/connmgr/connmgr.go
+++ b/p2p/net/connmgr/connmgr.go
@@ -243,19 +243,11 @@ type peerInfo struct {
 
 type peerInfos []peerInfo
 
-func (p peerInfos) SortByValue() {
-	sort.Slice(p, func(i, j int) bool {
-		left, right := p[i], p[j]
-		// temporary peers are preferred for pruning.
-		if left.temp != right.temp {
-			return left.temp
-		}
-		// otherwise, compare by value.
-		return left.value < right.value
-	})
-}
-
-func (p peerInfos) SortByValueAndStreams() {
+// SortByValueAndStreams sorts peerInfos by their value and stream count. It
+// will sort peers with no streams before those with streams (all else being
+// equal). If `sortByMoreStreams` is true it will sort peers with more streams
+// before those with fewer streams. This is useful to prioritize freeing memory.
+func (p peerInfos) SortByValueAndStreams(sortByMoreStreams bool) {
 	sort.Slice(p, func(i, j int) bool {
 		left, right := p[i], p[j]
 		// temporary peers are preferred for pruning.
@@ -278,12 +270,21 @@ func (p peerInfos) SortByValueAndStreams() {
 		}
 		leftIncoming, leftStreams := incomingAndStreams(left.conns)
 		rightIncoming, rightStreams := incomingAndStreams(right.conns)
+		// prefer closing inactive connections (no streams open)
+		if rightStreams != leftStreams && (leftStreams == 0 || rightStreams == 0) {
+			return leftStreams < rightStreams
+		}
 		// incoming connections are preferred for pruning
 		if leftIncoming != rightIncoming {
 			return leftIncoming
 		}
-		// prune connections with a higher number of streams first
-		return rightStreams < leftStreams
+
+		if sortByMoreStreams {
+			// prune connections with a higher number of streams first
+			return rightStreams < leftStreams
+		} else {
+			return leftStreams < rightStreams
+		}
 	})
 }
 
@@ -368,7 +369,7 @@ func (cm *BasicConnMgr) getConnsToCloseEmergency(target int) []network.Conn {
 	cm.plk.RUnlock()
 
 	// Sort peers according to their value.
-	candidates.SortByValueAndStreams()
+	candidates.SortByValueAndStreams(true)
 
 	selected := make([]network.Conn, 0, target+10)
 	for _, inf := range candidates {
@@ -398,7 +399,7 @@ func (cm *BasicConnMgr) getConnsToCloseEmergency(target int) []network.Conn {
 	}
 	cm.plk.RUnlock()
 
-	candidates.SortByValueAndStreams()
+	candidates.SortByValueAndStreams(true)
 	for _, inf := range candidates {
 		if target <= 0 {
 			break
@@ -459,7 +460,7 @@ func (cm *BasicConnMgr) getConnsToClose() []network.Conn {
 	}
 
 	// Sort peers according to their value.
-	candidates.SortByValue()
+	candidates.SortByValueAndStreams(false)
 
 	target := ncandidates - cm.cfg.lowWater
 
diff --git a/p2p/net/connmgr/connmgr_test.go b/p2p/net/connmgr/connmgr_test.go
index c2db206cb4..92c273c5f0 100644
--- a/p2p/net/connmgr/connmgr_test.go
+++ b/p2p/net/connmgr/connmgr_test.go
@@ -40,6 +40,15 @@ func (c *tconn) RemotePeer() peer.ID {
 	return c.peer
 }
 
+func (c *tconn) Stat() network.ConnStats {
+	return network.ConnStats{
+		Stats: network.Stats{
+			Direction: network.DirOutbound,
+		},
+		NumStreams: 1,
+	}
+}
+
 func (c *tconn) RemoteMultiaddr() ma.Multiaddr {
 	addr, err := ma.NewMultiaddr("/ip4/127.0.0.1/udp/1234")
 	if err != nil {
@@ -800,7 +809,7 @@ func TestPeerInfoSorting(t *testing.T) {
 		p1 := peerInfo{id: peer.ID("peer1")}
 		p2 := peerInfo{id: peer.ID("peer2"), temp: true}
 		pis := peerInfos{p1, p2}
-		pis.SortByValue()
+		pis.SortByValueAndStreams(false)
 		require.Equal(t, pis, peerInfos{p2, p1})
 	})
 
@@ -808,31 +817,67 @@ func TestPeerInfoSorting(t *testing.T) {
 		p1 := peerInfo{id: peer.ID("peer1"), value: 40}
 		p2 := peerInfo{id: peer.ID("peer2"), value: 20}
 		pis := peerInfos{p1, p2}
-		pis.SortByValue()
+		pis.SortByValueAndStreams(false)
 		require.Equal(t, pis, peerInfos{p2, p1})
 	})
 
-	t.Run("in a memory emergency, starts with incoming connections", func(t *testing.T) {
+	t.Run("prefer peers with no streams", func(t *testing.T) {
+		p1 := peerInfo{id: peer.ID("peer1"),
+			conns: map[network.Conn]time.Time{
+				&mockConn{stats: network.ConnStats{NumStreams: 0}}: time.Now(),
+			},
+		}
+		p2 := peerInfo{id: peer.ID("peer2"),
+			conns: map[network.Conn]time.Time{
+				&mockConn{stats: network.ConnStats{NumStreams: 1}}: time.Now(),
+			},
+		}
+		pis := peerInfos{p2, p1}
+		pis.SortByValueAndStreams(false)
+		require.Equal(t, pis, peerInfos{p1, p2})
+	})
+
+	t.Run("in a memory emergency, starts with incoming connections and higher streams", func(t *testing.T) {
 		incoming := network.ConnStats{}
 		incoming.Direction = network.DirInbound
 		outgoing := network.ConnStats{}
 		outgoing.Direction = network.DirOutbound
+
+		outgoingSomeStreams := network.ConnStats{Stats: network.Stats{Direction: network.DirOutbound}, NumStreams: 1}
+		outgoingMoreStreams := network.ConnStats{Stats: network.Stats{Direction: network.DirOutbound}, NumStreams: 2}
 		p1 := peerInfo{
 			id: peer.ID("peer1"),
 			conns: map[network.Conn]time.Time{
-				&mockConn{stats: outgoing}: time.Now(),
+				&mockConn{stats: outgoingSomeStreams}: time.Now(),
 			},
 		}
 		p2 := peerInfo{
 			id: peer.ID("peer2"),
+			conns: map[network.Conn]time.Time{
+				&mockConn{stats: outgoingSomeStreams}: time.Now(),
+				&mockConn{stats: incoming}:            time.Now(),
+			},
+		}
+		p3 := peerInfo{
+			id: peer.ID("peer3"),
 			conns: map[network.Conn]time.Time{
 				&mockConn{stats: outgoing}: time.Now(),
 				&mockConn{stats: incoming}: time.Now(),
 			},
 		}
-		pis := peerInfos{p1, p2}
-		pis.SortByValueAndStreams()
-		require.Equal(t, pis, peerInfos{p2, p1})
+		p4 := peerInfo{
+			id: peer.ID("peer4"),
+			conns: map[network.Conn]time.Time{
+				&mockConn{stats: outgoingMoreStreams}: time.Now(),
+				&mockConn{stats: incoming}:            time.Now(),
+			},
+		}
+		pis := peerInfos{p1, p2, p3, p4}
+		pis.SortByValueAndStreams(true)
+		// p3 is first because it is inactive (no streams).
+		// p4 is second because it has the most streams and we priortize killing
+		// connections with the higher number of streams.
+		require.Equal(t, pis, peerInfos{p3, p4, p2, p1})
 	})
 
 	t.Run("in a memory emergency, starts with connections that have many streams", func(t *testing.T) {
@@ -850,7 +895,7 @@ func TestPeerInfoSorting(t *testing.T) {
 			},
 		}
 		pis := peerInfos{p1, p2}
-		pis.SortByValueAndStreams()
+		pis.SortByValueAndStreams(true)
 		require.Equal(t, pis, peerInfos{p2, p1})
 	})
 }