Over the years, a variety of algorithms for finding frequent sequential patterns in very large sequential 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, patterns that contain only a few items will tend to be interesting if they have a high support, whereas long patterns can still be interesting even if their support is relatively small. Ideally, we desire to have an algorithm that finds all the frequent patterns whose support decreases as a function of their length. In this paper we present an algorithm called SLPMiner, that finds all sequential patterns that satisfy a length-decreasing support constraint. Our experimental evaluation shows that SLPMiner achieves up to two orders of magnitude of speedup by effectively exploiting the length-decreasing support constraint, and that its runtime increases gradually as the average length of the sequences (and the discovered frequent patterns) increases.