This paper considers the possibilities of randomized controls for designing confidence regions for unknown parameters. The assumptions about external noise that affect a linear plant are reduced to a minimum: external noise can virtually be arbitrary, but, independently of it, the user must be able to add test perturbations through the input channel. Based on a finite set of observations, we suggest a new procedure which can be used in adaptive control schemes. It has been developed in the general framework of "counting of leave-out sign-dominant correlation regions" (LSCR), which is mostly being promoted by M. Campi et al. for identification problems. The procedure returns confidence regions which are guaranteed to contain true parameters with a user-chosen probability. The theoretical results are illustrated by an example of a nonminimum-phase second-order plant.