Try to come up with the least controversial premise that you can use to support your argument, not just the first belief that comes to mind that will support it.

To use a (topical for me) example. someone at Giving What We Can might support effective charities "because it maximises expected utility so you're oblidged to do so, duh", but "if you can do a lot of good for little sacrifice, you should" is a better premise to rely on when talking to people in general, as it's weaker but still does the job.