This paper presents stopping rules and associated estimators, with prescribed mean squared errors, of the regression parameters in stochastic regression modles. The construction makes fundamental use of the martingale structure of least squares estimates or their modifications. For one-dimensional regressors, the stopping rules imply stop as soon as the conditional variance of the underlying martingale exceeds some suitably chosen threshold. We how this idea can be modified for the case of multidimensional stochastic regressors.