Should you always use 'int' for numbers in C, even if they are non-negative?

I always use unsigned int for values that should never be negative. But today I noticed this situation in my code:

void CreateRequestHeader( unsigned bitsAvailable, unsigned mandatoryDataSize, 
    unsigned optionalDataSize )
{
    If ( bitsAvailable – mandatoryDataSize >= optionalDataSize ) {
        // Optional data fits, so add it to the header.
    }

    // BUG! The above includes the optional part even if
    // mandatoryDataSize > bitsAvailable.
}

Should I start using int instead of unsigned int for numbers, even if they can't be negative?