It is considered good distributed computing practice to devise object implementations that tolerate contention, periods of asynchrony and a large number of failures, but perform fast if few failures occur, the system is synchronous and there is no contention. This paper initiates the first study of quorum systems that help design such implementations. Namely, our study of quorum systems encompasses, at the same time, the optimal resilience of distributed object implementations (just like traditional quorum systems), as well as their optimal best-case complexity (unlike traditional quorum systems). We introduce the notion of a refined quorum system (RQS) of some set S as a set of three refined classes of subsets (quorums) of S: first class quorums are also second class quorums, which are also third class quorums. First class quorums have large intersections with all other quorums, second class quorums might have slightly smaller intersections with those of the third class, the latter s...