Account for starting in phase 2

[emilgoldsmith]

This resolves #17

I'm not 100% confident in everything going on in the code, but since I ran some solver tests (I kept it ignored for Travis' sake, just ran them locally and they pass) I'm pretty confident my changes are correct. Please do double check that I didn't break something in init2 though!

This also includes the commit from #37 so that one should be merged first. Since they were different purposes I just thought it would be cleaner to break them up into two separate PRs.