Clowes [1] illustrated how to select the optimal time-scaling factor for approximations of rational transfer functions using a series expansion of Laguerre functions. This paper extends this result to approximations for general, L2 stable, linear systems. As a direct application of this extended result, we are able to obtain approximations for irrational transfer functions which minimize the frequency domain error in the L2 sense. Also, we will give empirical solutions for the optimal time-scaling factor for approximations of first order plus delay systems which can then be applied to a larger class of overdamped systems.