diff --git a/fs/accounting/stats.go b/fs/accounting/stats.go
index 4c44555f6..e41273ee8 100644
--- a/fs/accounting/stats.go
+++ b/fs/accounting/stats.go
@@ -13,6 +13,9 @@ import (
 	"github.com/rclone/rclone/fs/rc"
 )
 
+// Maximum number of completed transfers in startedTransfers list
+const maxCompletedTransfers = 100
+
 // StatsInfo accounts all transfers
 type StatsInfo struct {
 	mu                sync.RWMutex
@@ -560,10 +563,11 @@ func (s *StatsInfo) AddTransfer(transfer *Transfer) {
 	s.mu.Unlock()
 }
 
-// RemoveTransfer removes a reference to the started transfer.
-func (s *StatsInfo) RemoveTransfer(transfer *Transfer) {
-	s.mu.Lock()
-
+// removeTransfer removes a reference to the started transfer in
+// position i.
+//
+// Must be called with the lock held
+func (s *StatsInfo) removeTransfer(transfer *Transfer, i int) {
 	// add finished transfer onto old time ranges
 	start, end := transfer.TimeRange()
 	if end.IsZero() {
@@ -572,12 +576,33 @@ func (s *StatsInfo) RemoveTransfer(transfer *Transfer) {
 	s.oldTimeRanges = append(s.oldTimeRanges, timeRange{start, end})
 	s.oldTimeRanges.merge()
 
+	// remove the found entry
+	s.startedTransfers = append(s.startedTransfers[:i], s.startedTransfers[i+1:]...)
+}
+
+// RemoveTransfer removes a reference to the started transfer.
+func (s *StatsInfo) RemoveTransfer(transfer *Transfer) {
+	s.mu.Lock()
 	for i, tr := range s.startedTransfers {
 		if tr == transfer {
-			// remove the found entry
-			s.startedTransfers = append(s.startedTransfers[:i], s.startedTransfers[i+1:]...)
+			s.removeTransfer(tr, i)
 			break
 		}
 	}
 	s.mu.Unlock()
 }
+
+// PruneTransfers makes sure there aren't too many old transfers
+func (s *StatsInfo) PruneTransfers() {
+	s.mu.Lock()
+	// remove a transfer from the start if we are over quota
+	if len(s.startedTransfers) > maxCompletedTransfers+fs.Config.Transfers {
+		for i, tr := range s.startedTransfers {
+			if tr.IsDone() {
+				s.removeTransfer(tr, i)
+				break
+			}
+		}
+	}
+	s.mu.Unlock()
+}
diff --git a/fs/accounting/stats_groups.go b/fs/accounting/stats_groups.go
index 417f29511..dc77769ac 100644
--- a/fs/accounting/stats_groups.go
+++ b/fs/accounting/stats_groups.go
@@ -137,6 +137,8 @@ This returns stats about completed transfers:
 If group is not provided then completed transfers for all groups will be
 returned.
 
+Note only the last 100 completed transfers are returned.
+
 Parameters
 - group - name of the stats group (string)
 
diff --git a/fs/accounting/stats_test.go b/fs/accounting/stats_test.go
index 7afc78b46..5ae5ad956 100644
--- a/fs/accounting/stats_test.go
+++ b/fs/accounting/stats_test.go
@@ -7,6 +7,7 @@ import (
 	"time"
 
 	"github.com/pkg/errors"
+	"github.com/rclone/rclone/fs"
 	"github.com/rclone/rclone/fs/fserrors"
 	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
@@ -306,3 +307,30 @@ func TestTimeRangeDuration(t *testing.T) {
 	assert.Equal(t, 1*time.Second, makeTimeRanges(t, []string{"1-2"}).total())
 	assert.Equal(t, 91*time.Second, makeTimeRanges(t, []string{"1-2", "10-100"}).total())
 }
+
+func TestPruneTransfers(t *testing.T) {
+	max := maxCompletedTransfers + fs.Config.Transfers
+
+	s := NewStats()
+	for i := int64(1); i <= int64(max+100); i++ {
+		s.AddTransfer(&Transfer{
+			startedAt:   time.Unix(i, 0),
+			completedAt: time.Unix(i+1, 0),
+		})
+	}
+
+	s.mu.Lock()
+	assert.Equal(t, time.Duration(max+100)*time.Second, s.totalDuration())
+	assert.Equal(t, max+100, len(s.startedTransfers))
+	s.mu.Unlock()
+
+	for i := 0; i < 200; i++ {
+		s.PruneTransfers()
+	}
+
+	s.mu.Lock()
+	assert.Equal(t, time.Duration(max+100)*time.Second, s.totalDuration())
+	assert.Equal(t, max, len(s.startedTransfers))
+	s.mu.Unlock()
+
+}
diff --git a/fs/accounting/transfer.go b/fs/accounting/transfer.go
index 41a5536b3..9fc7f8f04 100644
--- a/fs/accounting/transfer.go
+++ b/fs/accounting/transfer.go
@@ -102,6 +102,8 @@ func (tr *Transfer) Done(err error) {
 		}
 		// Signal done with accounting
 		acc.Done()
+		// free the account since we may keep the transfer
+		acc = nil
 	}
 
 	tr.mu.Lock()
@@ -113,7 +115,7 @@ func (tr *Transfer) Done(err error) {
 	} else {
 		tr.stats.DoneTransferring(tr.remote, err == nil)
 	}
-	tr.stats.RemoveTransfer(tr)
+	tr.stats.PruneTransfers()
 }
 
 // Reset allows to switch the Account to another transfer method.