diff --git a/libtransmission/peer-mgr.c b/libtransmission/peer-mgr.c
index b26d27633..6070b4dfb 100644
--- a/libtransmission/peer-mgr.c
+++ b/libtransmission/peer-mgr.c
@@ -1727,11 +1727,20 @@ shouldPeerBeClosed( const Torrent * t, const tr_peer * peer, int peerCount )
         return TRUE;
     }
 
-    /* if we're both seeds and it's been long enough for a pex exchange, close it */
+    /* if we're seeding and the peer has everything we have,
+     * and enough time has passed for a pex exchange, then disconnect */
     if( 1 ) {
         const int clientIsSeed = tr_torrentIsSeed( tor );
-        const int peerIsSeed = atom->flags & ADDED_F_SEED_FLAG;
-        if( peerIsSeed && clientIsSeed && ( !tr_torrentAllowsPex(tor) || (now-atom->time>=30) ) ) {
+        int peerHasEverything;
+        if( atom->flags & ADDED_F_SEED_FLAG )
+            peerHasEverything = TRUE;
+        else {
+            tr_bitfield * tmp = tr_bitfieldDup( tr_cpPieceBitfield( tor->completion ) );
+            tr_bitfieldDifference( tmp, peer->have );
+            peerHasEverything = tr_bitfieldCountTrueBits( tmp ) == 0;
+            tr_bitfieldFree( tmp );
+        }
+        if( clientIsSeed && peerHasEverything && ( !tr_torrentAllowsPex(tor) || (now-atom->time>=30) ) ) {
             tordbg( t, "purging peer %s because we're both seeds", tr_peerIoAddrStr(&atom->addr,atom->port) );
             return TRUE;
         }
diff --git a/libtransmission/utils.c b/libtransmission/utils.c
index f804b962c..5a593ee1b 100644
--- a/libtransmission/utils.c
+++ b/libtransmission/utils.c
@@ -783,6 +783,20 @@ tr_bitfieldOr( tr_bitfield * a, const tr_bitfield * b )
     return a;
 }
 
+/* set 'a' to all the flags that were in 'a' but not 'b' */
+void
+tr_bitfieldDifference( tr_bitfield * a, const tr_bitfield * b )
+{
+    uint8_t *ait;
+    const uint8_t *aend, *bit;
+
+    assert( a->len == b->len );
+
+    for( ait=a->bits, bit=b->bits, aend=ait+a->len; ait!=aend; )
+        *ait++ &= ~(*bit++);
+}
+
+
 size_t
 tr_bitfieldCountTrueBits( const tr_bitfield* b )
 {
diff --git a/libtransmission/utils.h b/libtransmission/utils.h
index 8ced7755c..ebf5f937f 100644
--- a/libtransmission/utils.h
+++ b/libtransmission/utils.h
@@ -189,6 +189,7 @@ int  tr_bitfieldAdd( tr_bitfield*, size_t bit );
 int  tr_bitfieldRem( tr_bitfield*, size_t bit );
 int  tr_bitfieldAddRange( tr_bitfield *, size_t begin, size_t end );
 int  tr_bitfieldRemRange ( tr_bitfield*, size_t begin, size_t end );
+void tr_bitfieldDifference( tr_bitfield *, const tr_bitfield * );
 
 int    tr_bitfieldHas( const tr_bitfield*, size_t bit );
 int    tr_bitfieldIsEmpty( const tr_bitfield* );