If you were HDHP covered for only a few months at the end of 2015 (including December) and elected to use the Last Month Rule (LMR), you could make a 2015 contribution that exceeds the amount allowed for those few months of coverage. The LMR allows you to make up to a full year contribution and only be covered for December of the year. BUT, you must then remain eligible (have HDHP coverage) for the entire following year or else pay tax and penalty for making the LMR contribution for the previous year.