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Homology search is a key tool for understanding the role, structure, and biochemical function of genomic sequences. The most popular technique for rapid homology search is BLAST, which has been in widespread use within universities, research centers, and commercial enterprises since the early 1990s. We propose a new step in the BLAST algorithm to reduce the computational cost of searching with negligible effect on accuracy. This new step - semigapped alignment - compromises between the efficiency of ungapped alignment and the accuracy of gapped alignment, allowing BLAST to accurately filter sequences with lower computational cost. In addition, we propose a heuristic - restricted insertion alignment - that avoids unlikely evolutionary paths with the aim of reducing gapped alignment cost with negligible effect on accuracy. Together, after including an optimization of the local alignment recursion, our two techniques more than double the speed of the gapped alignment stages in blast. We conclude that our techniques are an important improvement to the BLAST algorithm. Source code for the alignment algorithms is available for download at http://www.bsg.rmit.edu.au/iga/.