Current process discovery techniques are unable to produce high quality models that describe all observed behavior in semi-structured processes in a meaningful way. Local process model (LPM) discovery has been proposed to discover meaningful patterns in event logs from unstructured processes. In this paper, we explore the use of LPM discovery on event logs from semi-structured processes and find several drawbacks: It finds many small patterns but doesn't find patterns larger than 4-5 events, it produces too many models, and the discovered models describe some events from the log multiple times while leaving others unexplained. Despite these drawbacks, we observe that a set of LPMs taken together can yield interesting insights. From these observations we distill several requirements for meaningful sets of LPMs: We want (1) a limited set of models that (2) have high accuracy measures such as fitness and precision while (3) they together cover the whole event log and (4) do not cover parts of the log multiple times unnecessarily. We show that it is possible to manually construct sets of LPMs that satisfy all these requirements on the well-known BPIC12 event log. We then apply and evaluate the existing quality measures for individual LPMs. We propose to disregard support, confidence, and determinism as measures for meaningfulness of LPMs and we propose new ways to evaluate sets of LPMs based existing methods.