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This paper presents a new algorithm, Hit-or-Jump, for embedded testing of components of communication systems that can be modeled by communicating extended finite state machines. It constructs test sequences efficiently with a high fault coverage. It does not have state space explosion, as is often encountered in exhaustive search, and it quickly covers the system components under test without being “trapped”, as is experienced by random walks. Furthermore, it is a generalization and unification of both exhaustive search and random walks; both are special cases of Hit-or-Jump. The algorithm has been implemented and applied to embedded testing of telephone services in an Intelligent Network (IN) architecture, including the Basic Call Service and five supplementary services.