IF with 3 possible solutions

Okay, I'm having trouble with this one. Here's what I want to do:

column A is my projection, column B is my allocation. I can't exceed my allocation, and I can't have a negative value.

In column C I want to put my value:
If A1 is greater than B1, I want to put B1.
If A1 is less than zero, I want to put 0.
If A1 is less than B1 but is equal or greater than 0 I want to put A1.

I tried to do it with an IF formula, but couldn't figure out how to get it with 3 possible results. Can anyone advise me?

Thanks,
John