Again, I said if they are expected to be operational for many weeks / months on end, you need a larger crew. You can't run people on 12-hour shifts (or 6-on/6-off) for long periods of time. Trust me on this; most of my 26-year military career was working rotating shifts to cover a 24/7/365 mission. I've been on several deployments and field exercises with minimum manning; I've worked plenty of 12-hour shifts. Two weeks with no days off is about the max a person can handle before starting to burn out. Tired people make mistakes. You don't want that in space.
If it's a small ship that has a home base, so it goes out and back for a few days (no more than about two weeks), then, sure, no problem with a small crew. You can reduce the duty positions by doubling up on tasks. Just put two people on the bridge, a pilot-in-command and co-pilot if you will. They will share flying, navigation, communications, and sensors. The ship's commander and second-in-command will work opposite shifts. I'd still want at least two people in the engine room at all times (save for quick restroom / meal breaks). Ergo, if you're insisting on 12-hour shifts (or 6&6), then you only need two teams of four people. There's eight of your crew. So, yes, you can make it work with 12-15 people.
On the other hand, if this was my ship/story (but it's not!), I would go with three teams, and at least a third person on the bridge, which brings it up to 15 people. I'd round the crew out with another 6 to 10 specialists (medic, gunners, etc), or more depending on the mission statement and combat capabilities of the ship. The ship I'm writing about is a patrol cutter with a crew of about a hundred. It's small but is still a fully capable warship that goes out for six months or more at a time, so it has three 5-man teams each on the bridge and in engineering, accounting for a third of the crew.