The PPSZ Algorithm presented by Paturi, Pudlak, Saks, and Zane in 1998 has the nice feature that the only satisfying solution of a uniquely satisfiable $3$-SAT formula can be found in expected running time at most $O(1.3071^n)$. Its bound degenerates when the number of solutions increases. In 1999, Schöning proved an bound of $\O(1.3334^n)$ for $3$-SAT. In 2003, Iwama and Tamaki combined both algorithms to yield an $O(1.3238^n)$ bound. We tweak the PPSZ-Bound to get a slightly better contribution to the combined algorithm and prove an $\O(1.32216^n)$ bound.