Hi Snowfrog
Here is an excellent care sheet for bettas:
Welcome and Betta Care Guide - Please Read First!!!
You'll notice that it says 2.5g is the minimum tank recommended; bettas are tropical fish, which means they need warm water to live happily and ward off any diseases (like
ICH). Any smaller tank, and the heater can't keep the water at a warm, stable temp. Also, less water means it's much harder to keep the water clean and free of
ammonia build-up (which comes when fish poop and fish food deteriorate in the water).
Is it possible to exchange your current setup for a slightly larger all-in-one version (like a 3g or 5g)? If you want corydoras (or otos might work) as tanks mates, the minimum tank size is about 10g because corydoras needs to be with others of their kind and they need a large footprint. I really wouldn't suggest any other fish as a tank mate; bettas are definitely solo swimmers because of their aggression.
Before you add a fish, I suggest this link:
http://www.fishlore.com/NitrogenCycle.htm Basically, before you add fish, you want the tank to build up the proper bacteria that will convert fish waste into a much less toxic substance. You achieve this beneficial bacteria by going through the
nitrogen cycle.
That's a whole lotta info to throw out there, so if you have more questions or need insights, explanations, or anything, just ask. We are all just here to help out as much as we can.
