peerconn.go         | 18 ++++++++++++------
 request-strategy.go |  4 ++++

diff --git a/peerconn.go b/peerconn.go
index 71ac5f3d252a230d4b7bbed38ae9033e41d30e52..f3680e1832472b6e893c2784a4ddcc621bc42dd1 100644
--- a/peerconn.go
+++ b/peerconn.go
@@ -47,6 +47,10 @@ type PeerRemoteAddr interface {
 	String() string
 }
 
+// Since we have to store all the requests in memory, we can't reasonably exceed what would be
+// indexable with the memory space available.
+type maxRequests = int
+
 type Peer struct {
 	// First to ensure 64-bit alignment for atomics. See #262.
 	_stats ConnStats
@@ -83,9 +87,10 @@ 	lastStartedExpectingToReceiveChunks time.Time
 	cumulativeExpectedToReceiveChunks   time.Duration
 	_chunksReceivedWhileExpecting       int64
 
-	choking          bool
-	requests         map[Request]struct{}
-	requestsLowWater int
+	choking                                bool
+	requests                               map[Request]struct{}
+	piecesReceivedSinceLastRequestUpdate   maxRequests
+	maxPiecesReceivedBetweenRequestUpdates maxRequests
 	// Chunks that we might reasonably expect to receive from the peer. Due to
 	// latency, buffering, and implementation differences, we may receive
 	// chunks that are no longer in the set of requests actually want.
@@ -114,7 +119,7 @@ 	// Pieces we've accepted chunks for from the peer.
 	peerTouchedPieces map[pieceIndex]struct{}
 	peerAllowedFast   bitmap.Bitmap
 
-	PeerMaxRequests  int // Maximum pending requests the peer allows.
+	PeerMaxRequests  maxRequests // Maximum pending requests the peer allows.
 	PeerExtensionIDs map[pp.ExtensionName]pp.ExtensionNumber
 	PeerClientName   string
 
@@ -470,8 +475,8 @@ 	return index < len(cn.metadataRequests) && cn.metadataRequests[index]
 }
 
 // The actual value to use as the maximum outbound requests.
-func (cn *Peer) nominalMaxRequests() (ret int) {
-	return int(clamp(1, int64(cn.PeerMaxRequests), 64))
+func (cn *Peer) nominalMaxRequests() (ret maxRequests) {
+	return int(clamp(1, 2*int64(cn.maxPiecesReceivedBetweenRequestUpdates), int64(cn.PeerMaxRequests)))
 }
 
 func (cn *Peer) totalExpectingTime() (ret time.Duration) {
@@ -1358,6 +1363,7 @@
 	c.allStats(add(1, func(cs *ConnStats) *Count { return &cs.ChunksReadUseful }))
 	c.allStats(add(int64(len(msg.Piece)), func(cs *ConnStats) *Count { return &cs.BytesReadUsefulData }))
 	if deletedRequest {
+		c.piecesReceivedSinceLastRequestUpdate++
 		c.allStats(add(int64(len(msg.Piece)), func(cs *ConnStats) *Count { return &cs.BytesReadUsefulIntendedData }))
 	}
 	for _, f := range c.t.cl.config.Callbacks.ReceivedUsefulData {
diff --git a/request-strategy.go b/request-strategy.go
index 7c7660bc4cc83d705a8c38541c5ad835fff2a0d7..f0470007ccf91d58567c2b54b62f3862b0a96751 100644
--- a/request-strategy.go
+++ b/request-strategy.go
@@ -53,6 +53,10 @@ 		t.iterPeers(func(p *Peer) {
 			if p.closed.IsSet() {
 				return
 			}
+			if p.piecesReceivedSinceLastRequestUpdate > p.maxPiecesReceivedBetweenRequestUpdates {
+				p.maxPiecesReceivedBetweenRequestUpdates = p.piecesReceivedSinceLastRequestUpdate
+			}
+			p.piecesReceivedSinceLastRequestUpdate = 0
 			rst.Peers = append(rst.Peers, request_strategy.Peer{
 				HasPiece:    p.peerHasPiece,
 				MaxRequests: p.nominalMaxRequests(),