The statistical significance of gapped local alignments is characterized by analyzing the extremal statistics of the scores obtained from the alignment of random amino acid sequences. By identifying a complete set of linked clusters, "islands," we devise a method which accurately predicts the extremal score statistics by using only one to a few pairwise alignments. The success of our method relies crucially on the link between the statistics of island scores and extremal score statistics. This link is motivated by heuristic arguments, and firmly established by extensive numerical simulations for a variety of scoring parameter settings and sequence lengths. Our approach is several orders of magnitude faster than the widely used shuffling method, since island counting is trivially incorporated into the basic Smith-Waterman alignment algorithm with minimal computational cost, and all islands are counted in a single alignment. The availability of a rapid and accurate significance estimation method gives one the flexibility to fine tune scoring parameters to detect weakly homologous sequences and obtain optimal alignment fidelity.