Motivated by the identification of the musical structure of pop songs, we introduce combinatorial problems involving overlays (non-overlapping substrings) and the covering of a text t by them. We present 4 problems and suggest solu- tions based on string pattern matching techniques. We show that decision problems of this type can be solved using an Aho-Corasick keyword automaton. We conjecture that one general optimization problem of the type, is NP-complete and introduce a simpler, more pragmatic optimization prob- lem. We solve the latter using suffix trees and finally, we suggest other open problems for further investigation.