Earlier approaches to random compact testing use a random pattern generator which depends on the combinational function under test and a circuit signature which remains the same independent of the circuit. In this correspondence we analyze the performance of a new scheme in which the pattern generator is simple and independent of the function being tested but the circuit signature is chosen to be a coefficient from the Rademacher-Walsh (RW) spectrum of the function under test. The analysis provides guidelines for choosing an RW coefficient, a test length, and an error tolerance so as to minimize the probabilities of rejecting a good unit or accepting a faulty one.