Arithmetics with carry

I'm designing a processor for one specific application and in my
software I have need a counter. I have a problem figuring out how to
make Add-with-carry work for this.

I want to do v := v + i.
v and i are both 32 bit values, my ALU is 16 bits wide.
Everything is 2-complement.

I would add the lower 16 bits, then add the higher 16 bits with carry.
My problem: "i" may be positive or negative, so there are 3 things
that can occur:
- overflow
- underflow
- none of those

If I have only one carry bit, those 3 possibilities cannot be
represented. Am I right that in such an architecture it is impossible
to achieve what I want? How do I have to change my ALU in order to do
that? And how do I handle the sign bits in the "middle" of the 32 bit
values? If possible, I would like to avoid an additional comparison
and use only flags.

I have looked at PicoBlaze as an example, but I could not figure out
what I am doing wrong. Please help :) Thanks, Dan