Recursive identification algorithms contain a number of "tuning parameters" to be chosen by the user. Two important such choices are the search direction (the direction in which the estimates are updated) and the gain sequence (the step length). In this paper a family of recursive (prediction error) identification algorithms is considered. The asymptotic distribution of the obtained estimates is derived. It is shown that a gain sequence decaying as 1/t and the Gauss-Newton search direction yields optimal asymptotic accuracy (meeting the Cramér-Rao theoretical lower bound). It is also shown that these are essentially the only asymptotic choices of direction and gains that give this optimal accuracy.