Background: Computational discovery of motifs in biomolecular sequences is an established field, with applications both in the discovery of functional sites in proteins and regulatory sites in DNA. In recent years there has been increased attention towards the discovery of composite motifs, typically occurring in cis-regulatory regions of genes. Results: This paper describes Compo: a discrete approach to composite motif discovery that supports richer modeling of composite motifs and a more realistic background model compared to previous methods. Furthermore, multiple parameter and threshold settings are tested automatically, and the most interesting motifs across settings are selected. This avoids reliance on single hard thresholds, which has been a weakness of previous discrete methods. Comparison of motifs across parameter settings is made possible by the use of p-values as a general significance measure. Compo can either return an ordered list of motifs, ranked according to the gen...