Algebraic cryptanalysis can be used to break (small versions of) block ciphers with small data complexity. If we have access to a large number of P-C pairs, algebraic cryptanalysis can be combined with differential techniques. Differential characteristic produces extra linear equations, which can be used to augment the original algebraic system. In our experiments with algebraic differential cryptanalysis, we have developed a different technique to represent the system. In our new method, we model a single P-C pair based encryption, but we use the differential to restrict the equations that model active S-boxes. An algebraic system created with our new model is smaller, and can theoretically be solved faster. Our experiments show that the advantage depends on the overall number of P-C pairs available and whether the chosen differential characteristic is correctly estimated. One of the advantages of the new method is that it can use partial information from the differential and still determine a correct solution faster than both the standard algebraic attack and the standard algebraic-differential attack.