We introduce a new approach to computing abstractions for mixed discrete-continuous systems. The abstractions try to capture the reachability information relevant for a given safety property as succinctly as possible. This is achieved by an incremental refinement of the abstractions, simultaneously trying to avoid increases in their size as much as possible. The approach does not depend on a concrete technique for computing reachability information, but only requires abstract operations fulfilling certain properties. Hence it can be used for various models of mixed discrete-continuous systems for which a concrete (approximate) reachability computation technique fulfilling those properties is provided.