Specification mining methods are used to extract candidate specifications from system execution traces. A major challenge for specification mining is succinctness. That is, in addition to the soundness, completeness, and scalable performance of the specification mining method, one is interested in producing a succinct result, which conveys a lot of information about the system under investigation but uses a short, machine and human-readable representation. In this paper we address the succinctness challenge in the context of scenario-based specification mining, whose target formalism is live sequence charts (LSC), an expressive extension of classical sequence diagrams. We do this by adapting three classical notions: a definition of an equivalence relation over LSCs, a definition of a redundancy and inclusion relation based on isomorphic embeddings among LSCs, and a delta-discriminative measure based on an information gain metric on a sorted set of LSCs. These are applied on top of the commonly used statistical metrics of support and confidence. A number of case studies show the utility of our approach towards succinct mined specifications.