The purpose of this paper is to introduce a certain modification to the technique of ridge analysis. The standard ridge analysis is employed in order to find conditions on a set of design variables that maximize (or minimize) an estimated second order response function on spheres of varying radii. See for example [3], [4], and [6]. The standard ridge analysis does not account for the fact that the experimental design (or lack of design) might result in large fluctuations in the variance of the predicted response on a sphere of a given radius. Thus the technique might well produce poor estimates of maximum responses and also conditions that give rise to it. Obviously one can expect the difficulty when non-rotatable designs are used to estimate the second order function. In this paper the precision of the predicted response is given a serious consideration in the search for optimum operating conditions. We consider two cases, one in which the variance contours are ellipsoidal, and the more general (and perhaps more typical) experimental situation in which there is no systematic experimental design. In the latter case, the suggested modification is to reduce the influence of the variance of the predicted response by restraining a certain portion of it, that which corresponds to the smallest eigenvalue of the moment matrix. Examples are given for both the specific and general cases to illustrate the improvement over the standard ridge analysis.