Over the years, a variety of algorithms for finding frequent itemsets in very large transaction databases have been developed. The key feature in most of these algorithms is that they use a constant support constraint to control the inherently exponential complexity of the problem. In general, itemsets that contain only a few items will tend to be interesting if they have a high support, whereas long itemsets can still be interesting even if their support is relatively small. Ideally, we desire to have an algorithm that finds all the frequent itemsets whose support decreases as a function of their length. In this paper we present an algorithm called LPMinel, that finds all itemsets that satisfy a length-decreasing support constraint. Our experimental evaluation shows that LPMiner is up to two orders of magnitude faster than the FP-growth algorithm for finding itemsets at a constant support constraint, and that its runtime increases gradually as the average length of the transactions (and the discovered itemsets) increases.