A central part of many algorithms for mining association rules in large data sets is a procedure that finds so called frequent itemsets. This paper proposes a new approach to finding frequent itemsets. The approach reduces a number of passes through an input data set and generalises a number of strategies proposed so far. The idea is to analyse a variable number n of itemset lattice levels in p scans through an input data set. It is shown that for certain values of parameters (n,p) this method provides more flexible utilisation of fast access transient memory and faster elimination of itemsets with low support factor. The paper presents the results of experiments conducted to find how the performance of the association rule mining algorithm depends on the values of parameters (n,p).