Classical frequentist statistics can lead to tortured conclusions when a study is complicated by having more than two treatment arms, several interim analyses, and a host of secondary outcomes. A series of influential papers has shown how difficult it is to ensure strict control of Type I error rate in such situations. We present several examples illustrating that integrating “what the data seem to be trying to say” with the rules governing multiplicity is so difficult that it raises the question of when strict control is necessary. Of special interest are studies that stop early for convincing evidence of benefit on the primary outcome but their structure is such that claims for secondary outcomes cannot be made with statistical rigor. We pose – with some trepidation – the question of when looser “control” is scientifically acceptable.