Some nights no bother at all - I've been getting way more of these nights on meds than off, others it'll be a 3am one (2-3am has been my norm for as long as I can remember so it's not made it worse as such), and on the odd occasion I'll keep myself busy with something all night and do a double day.
Unfortunately no solid answer there, I take the meds first thing in the morning and hope I'll be able get to sleep later. Fortunately (for me) this has been my norm for as long as I can remember either way so at least nothing is worse!