A sufficient condition for consistent estimates of parametera in linear S.I.S.O. system identification is that the input signal should be ‘ persistently exciting ’, However,. in practice the exact nature of the test signal has a direct bearing upon the identification accuracy. This paper shows howa-prioriknowledge of the approximate system and noise model parameters may be used to design a test signal which will minimize the variance of the parameter estimates. The design procedure is computationally efficient as full advantage is taken of the special structure of linear S.I.S.O. systems. The optimal test signals are shown to result in a significant reduction in the parameter variances. This is of considerable practical importance as either the experiment time may be reduced for the same model accuracy or for fixed experiment time a model of much higher accuracy may be obtained.