diff --git a/xwords4/common/model.c b/xwords4/common/model.c
index 76dbe316e..eadeb0ace 100644
--- a/xwords4/common/model.c
+++ b/xwords4/common/model.c
@@ -1838,7 +1838,7 @@ model_assignPlayerTiles( ModelCtxt* model, XP_S16 turn,
 {
     XP_ASSERT( turn >= 0 );
     TrayTileSet sorted;
-    sortTiles( &sorted, tiles );
+    sortTiles( &sorted, tiles, 0 );
     stack_addAssign( model->vol.stack, turn, &sorted );
 
     assignPlayerTiles( model, turn, tiles );
@@ -1850,7 +1850,8 @@ model_sortTiles( ModelCtxt* model, XP_S16 turn )
     XP_S16 nTiles;
 
     TrayTileSet sorted;
-    sortTiles( &sorted, model_getPlayerTiles( model, turn ) );
+    const TrayTileSet* curTiles = model_getPlayerTiles( model, turn );
+    sortTiles( &sorted, curTiles, XP_MIN( 3, curTiles->nTiles) );
 
     nTiles = sorted.nTiles;
     while ( nTiles > 0 ) {
diff --git a/xwords4/common/movestak.c b/xwords4/common/movestak.c
index 7f3397023..401927347 100644
--- a/xwords4/common/movestak.c
+++ b/xwords4/common/movestak.c
@@ -97,7 +97,7 @@ augmentFor( XP_U32 hash, const StackEntry* entry )
     switch( entry->moveType ) {
     case ASSIGN_TYPE: {
         TrayTileSet tiles;
-        sortTiles( &tiles, &entry->u.assign.tiles );
+        sortTiles( &tiles, &entry->u.assign.tiles, 0 );
         hash = augmentHash( hash, (XP_U8*)&tiles, sizeof(tiles) );
     }
         break;
diff --git a/xwords4/common/strutils.c b/xwords4/common/strutils.c
index 4b1cd48b9..6ccd67673 100644
--- a/xwords4/common/strutils.c
+++ b/xwords4/common/strutils.c
@@ -84,13 +84,18 @@ removeTile( TrayTileSet* tiles, XP_U16 index )
 }
 
 void
-sortTiles( TrayTileSet* dest, const TrayTileSet* src )
+sortTiles( TrayTileSet* dest, const TrayTileSet* src, XP_U16 skip )
 {
+    XP_ASSERT( src->nTiles >= skip );
     TrayTileSet tmp = *src;
-    dest->nTiles = 0;
-    while ( 0 < tmp.nTiles ) {
+
+    /* Copy in the ones we're not sorting */
+    dest->nTiles = skip;
+    XP_MEMCPY( &dest->tiles, &tmp.tiles, skip * sizeof(tmp.tiles[0]) );
+
+    while ( skip < tmp.nTiles ) {
         XP_U16 ii, smallest;
-        for ( smallest = ii = 0; ii < tmp.nTiles; ++ii ) {
+        for ( smallest = ii = skip; ii < tmp.nTiles; ++ii ) {
             if ( tmp.tiles[ii] < tmp.tiles[smallest] ) {
                 smallest = ii;
             }
diff --git a/xwords4/common/strutils.h b/xwords4/common/strutils.h
index b4a200fb7..00e2e6116 100644
--- a/xwords4/common/strutils.h
+++ b/xwords4/common/strutils.h
@@ -34,7 +34,7 @@ XP_U16 bitsForMax( XP_U32 n );
 
 void traySetToStream( XWStreamCtxt* stream, const TrayTileSet* ts );
 void traySetFromStream( XWStreamCtxt* stream, TrayTileSet* ts );
-void sortTiles( TrayTileSet* dest, const TrayTileSet* src );
+void sortTiles( TrayTileSet* dest, const TrayTileSet* src, XP_U16 skip );
 void removeTile( TrayTileSet* tiles, XP_U16 index );
 
 XP_S32 signedFromStream( XWStreamCtxt* stream, XP_U16 nBits );