The Four Russians technique is a method that divides a sequence alignment problem into tiles and uses a precomputed lookup table to quickly find the solution to each tile. By dividing the dynamic programming table into tiles of size t_n × t_m , the running time of the alignment algorithm is reduced to O(nm/(t_nt_m)). We explore this technique as it applies to the problem of genomic sequence alignment. Beyond the simple global alignment problem, we implement the Four Russians technique for a banded extension algorithm, which only covers a diagonal band of the dynamic programming table and, similar to local alignment, extends an alignment ending anywhere in the table, and an early dropout algorithm similar to X-Drop. Using a t₃ × t₃ sized tile, the average speedup was 5.15 for the Needleman-Wunsch full global alignment algorithm, 2.98 for the banded extension algorithm, and 2.77 for the X-Drop algorithm, running over data produced by the PBSIM synthetic generator.