The problem of extracting all association rules from within a binary database is well-known. Existing methods may involve multiple passes of the database, and cope badly with densely- packed database records because of the combinatorial explosion in the number of sets of attributes for which incidence-counts must be computed. We describe here a class of methods we have introduced that begin by using a single database pass to perform a partial computation of the totals required, storing these in the form of a set enumeration tree, which is created in time linear to the size of the database. Algorithms for using this structure to complete the count summations are discussed, and a method is described, derived from the well-known Apriori algorithm. Results are presented demonstrating the performance advantage to be gained from the use of this approach.