Mulligans
General Mulligans
You basically want to keep whatever you want to have before you snap. Sense Demons comes in handy to get Betrug/Jaraxxus and heal from Aranasi Broodmother.
Aggro Mulligans
Against aggro you need to make sure you can safely snap. Because of perfect synergy with curve Lord Godfrey can even be considered to keep.
Try to make sure you have either Archivist Elysiana or Plot Twist + Augmented Elekk before you use Void Contract.