This paper presents an analysis of how maximally general and accurate rules can be evolved in a Pittsburgh-style classifier system. In order to be able to perform such an analysis we introduce a simple bare-bones Pittsburgh-style classifier systems - the compact classifier system (CCS) - based on estimation of distribution algorithms. Using a common rule encoding schemes of Pittsburgh-style classifier systems, CCS maintains a dynamic set of probability vectors that compactly describe a rule set. The compact genetic algorithm is used to evolve each of the initially perturbated probability vectors. Results show how CCS is able to evolve in a compact, simple, and elegant manner rule sets composed by maximally general and accurate rules. The initial theoretical analysis and results also show that traditional encoding schemes used by Pittsburgh-style classifiers add an extra facet of difficulty. Such a bias plays a central role on the overall performance and scalability of CCS and other Pittsburgh-style systems using such encoding schemes