cmd/tracker-announce/main.go |  6 +++---
 torrent.go                   | 10 +++++-----
 tracker/http.go              | 12 +++++++++++-
 tracker/tracker.go           |  2 +-

diff --git a/cmd/tracker-announce/main.go b/cmd/tracker-announce/main.go
index f2eb02e419708bf8029af9924e96554aa49f957a..4c029c39d18fba2722c6dfbda54e9d57d77d23c8 100644
--- a/cmd/tracker-announce/main.go
+++ b/cmd/tracker-announce/main.go
@@ -2,16 +2,16 @@ package main
 
 import (
 	"log"
-	"math"
 	"net/url"
 	"strings"
 	"sync"
+
+	"github.com/davecgh/go-spew/spew"
 
 	"github.com/anacrolix/tagflag"
 	"github.com/anacrolix/torrent"
 	"github.com/anacrolix/torrent/metainfo"
 	"github.com/anacrolix/torrent/tracker"
-	"github.com/davecgh/go-spew/spew"
 )
 
 func argSpec(arg string) (ts *torrent.TorrentSpec, err error) {
@@ -37,7 +37,7 @@ 	}
 	tagflag.Parse(&flags)
 	ar := tracker.AnnounceRequest{
 		NumWant: -1,
-		Left:    math.MaxUint64,
+		Left:    -1,
 		Port:    flags.Port,
 	}
 	var wg sync.WaitGroup
diff --git a/torrent.go b/torrent.go
index 33f43b30bcef09240250573eeaae219d5830a873..15029945d1af9db6e5f190e8562349145c45d0f1 100644
--- a/torrent.go
+++ b/torrent.go
@@ -6,7 +6,6 @@ 	"crypto/sha1"
 	"errors"
 	"fmt"
 	"io"
-	"math"
 	"math/rand"
 	"net/url"
 	"os"
@@ -14,6 +13,8 @@ 	"sync"
 	"text/tabwriter"
 	"time"
 	"unsafe"
+
+	"github.com/davecgh/go-spew/spew"
 
 	"github.com/anacrolix/dht"
 	"github.com/anacrolix/log"
@@ -28,7 +29,6 @@ 	"github.com/anacrolix/torrent/metainfo"
 	pp "github.com/anacrolix/torrent/peer_protocol"
 	"github.com/anacrolix/torrent/storage"
 	"github.com/anacrolix/torrent/tracker"
-	"github.com/davecgh/go-spew/spew"
 )
 
 func (t *Torrent) chunkIndexSpec(chunkIndex pp.Integer, piece pieceIndex) chunkSpec {
@@ -635,11 +635,11 @@ 	return
 }
 
 // Bytes left to give in tracker announces.
-func (t *Torrent) bytesLeftAnnounce() uint64 {
+func (t *Torrent) bytesLeftAnnounce() int64 {
 	if t.haveInfo() {
-		return uint64(t.bytesLeft())
+		return t.bytesLeft()
 	} else {
-		return math.MaxUint64
+		return -1
 	}
 }
 
diff --git a/tracker/http.go b/tracker/http.go
index 87927e773214ba348cadb1b09cf98e6c956f766b..65cb198956b06608a1b5465cfa05b11cf0544d54 100644
--- a/tracker/http.go
+++ b/tracker/http.go
@@ -5,6 +5,7 @@ 	"bytes"
 	"crypto/tls"
 	"fmt"
 	"io"
+	"math"
 	"net"
 	"net/http"
 	"net/url"
@@ -74,7 +75,16 @@ 	// AFAICT, port is mandatory, and there's no implied port key.
 	q.Set("port", fmt.Sprintf("%d", ar.Port))
 	q.Set("uploaded", strconv.FormatInt(ar.Uploaded, 10))
 	q.Set("downloaded", strconv.FormatInt(ar.Downloaded, 10))
-	q.Set("left", strconv.FormatUint(ar.Left, 10))
+
+	// The AWS S3 tracker returns "400 Bad Request: left(-1) was not in the valid range 0 -
+	// 9223372036854775807" if left is out of range, or "500 Internal Server Error: Internal Server
+	// Error" if omitted entirely.
+	left := ar.Left
+	if left < 0 {
+		left = math.MaxInt64
+	}
+	q.Set("left", strconv.FormatInt(left, 10))
+
 	if ar.Event != None {
 		q.Set("event", ar.Event.String())
 	}
diff --git a/tracker/tracker.go b/tracker/tracker.go
index 446e2cb295ba9b8b283a477919c6ade4c5674072..c3eefb98d929957f569fda9280275ac6aee576e7 100644
--- a/tracker/tracker.go
+++ b/tracker/tracker.go
@@ -14,7 +14,7 @@ type AnnounceRequest struct {
 	InfoHash   [20]byte
 	PeerId     [20]byte
 	Downloaded int64
-	Left       uint64
+	Left       int64 // If less than 0, math.MaxInt64 will be used for HTTP trackers instead.
 	Uploaded   int64
 	// Apparently this is optional. None can be used for announces done at
 	// regular intervals.