We give estimates for the running time of the function field sieve (FFS) to compute discrete logrithms in F for small p. Specifically. we obtain probability estimates that allow us to select optimal parameters in cases of cryptographic interest, wihout appealing to the heuristic commonly relied upon in an asymplotic anallysis. We also give evidence that for any fixed size some many be weaker than others of the different characteristic or field representation, and compare the relation difficulty of computing discrete logarithme via the FFS a such came