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A large variety of methods have been proposed for the generation of pseudoexhaustive test sets for the built-in selftest of combinational circuits. The test pattern generator, in most all of the methods, is some form of linear feedback register (LFSR). In this work, we concentrate on a simple LFSR structure, known as LFSRISR, and show that particular orderings of the LFSR cells can significantly reduce the test set size. In addition, we show for the first time that an LFSRISR designed with a particular cell ordering and the allowance of a marginal number of additional cells guarantees pseudoexhaustive test sets of the minimum size 2", where w is the maximum input dependency limit of the circuit under test. Extensive experimentation on benchmark circuits and comparisons with the hardware overhead of other methods indicate the advantage of this approach.