A new set of modals is appearing in contemporary English. The epistemic modals with perfect have are forming a new class including mighta, coulda, woulda, shoulda, and musta, when they are used with an additional have and without a (present) perfect meaning. I look at their structure and examine possible determinacy violations when they (and the core modals) move to C. The data come from corpus and internet sources; the study is not a quantitative one because the change is not yet particularly frequent.