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.