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Finite State Machines (FSMs) are widely used to generate test case suites for critical systems. Several test case generation methods are derived from the well-known W-method. The Wp-method is a variation of the W-method, which produces smaller test suites. The G-method is a generalization of the W-method, which dispenses the use of characterization sets. In this paper, we combine ideas of both, and introduce a new generalized method, that does not depend on characterization sets, as the Wp-method does, and may produce smaller test suites than those of the G-method.