It sounds like you are using touch to drag the tiles, am I correct. It should be the only case where the tile need to be dragged a bit up or down in order to initiate the drag. Is that correct? If that is the case, there isn't much you can do at the moment, since disabling that behavior will also disable the Touch Scrolling functionality. Nevertheless, we are currently working on a more friendly Touch API that will enable the more precise manipulation of the behavior.
Hope this makes sense.
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