Building on previous literature I argue that the principle Maximize Presupposition! as standardly conceived is too permissive in that it sanctions certain utterances that are intuitively infelicitous. I propose as an alternative to MP a novel principle called Logical Integrity and I showed that while LI makes the same prediction as MP for the basic cases it is restrictive enough to account for the problematic cases discussed. Furthermore, I argue that LI without further ado make interesting predictions for a novel type of example, the cases discussed in Magri (2009), and Hurford's Constraint. Finally, I discuss and defused one potential counter-example to LI.