Background distribution statistics for profile-based sequence alignment algorithms cannot be calculated analytically, and hence such algorithms must resort to measuring the significance of an alignment score by assessing its location among a distribution of background alignment scores. The Gumbel parameters that describe this background distribution are usually pre-computed for a limited number of scoring systems, gap schemes, and sequence lengths and compositions. The use of such look-ups is known to introduce errors, which compromise the significance assessment of a remote homology relationship. One solution is to estimate the background distribution for each pair of interest by generating a large number of sequence shuffles and use the distribution of their scores to approximate the parameters of the underlying extreme value distribution. This is computationally very expensive, as a large number of shuffles are needed to precisely estimate the score statistics.