Cooperatively acting pairs of cis-regulatory elements play important roles in many biological processes. Here, we describe a statistical approach, compositionally orthogonalized co-occurrence analysis (coCOA) that detects pairs of oligonucleotides that preferentially co-occur in pairs of sequence regions, controlling for correlations between the compositions of the analyzed regions. coCOA identified three clusters of oligonucleotide pairs that frequently co-occur at 5′ and 3′ ends of human and mouse introns. The largest cluster involved GC-rich sequences at the 5′ ends of introns that co-occur and are co-conserved with specific AU-rich sequences near intron 3′ ends. These motifs are preferentially conserved when they occur together, as measured by a new co-conservation measure, supporting common in vivo function. These motif pairs are also enriched in introns flanking alternative "cassette" exons, suggesting a role in silencing of intervening exons, and we showed that these motifs can cooperatively silence splicing of an intervening exon in a splicing reporter assay. This approach can be easily generalized to problems beyond RNA splicing.