We study voting games on binary issues, where voters hold an objective over the outcome of the collective decision and are allowed, before the vote takes place, to negotiate their ballots with the other participants. We analyse the voters' rational behaviour in the resulting two-phase game when ballots are aggregated via non-manipulable rules and, more specifically, quota rules. We show under what conditions undesirable equilibria can be removed and desirable ones sustained as a consequence of the pre-vote phase.