In the context of increasing automation of Australian electoral processes, and accusations of deliberate interference in elections in Europe and the USA, it is worthwhile understanding how little a change in the recorded ballots could change an election result. In this paper we construct manipulations of the ballots in order to change the overall balance of power in an Australian Federal Senate election – the upper house of Parliament. This gives, hopefully tight, over-estimations of the Margin of Victory (MOV) for the party or coalition winning the Senate. This is critical information for determining how well we can trust the reported results, and how much auditing should be applied to the election process to be certain that it reports the true result. The challenge arising in Australian Federal Senate elections is that they use a complicated Single Transferable Vote (STV) method for which it is intractable to compute the true MOV, hence we must rely on greedy methods to find small manipulations.