Local Process Models (LPM) describe structured fragments of process behavior occurring in the context of less structured business processes. Traditional LPM discovery aims to generate a collection of process models that describe highly frequent behavior, but these models do not always provide useful answers to questions posed by process analysts aiming at business process improvement. We propose a framework for goal-driven LPM discovery, based on utility functions and constraints. We describe four scopes on which these utility functions and constraints can be defined, and show that utility functions and constraints on different scopes can be combined to form composite utility functions/constraints. Finally, we demonstrate the applicability of our approach by presenting several actionable business insights discovered with LPM discovery on three real-life data sets.