This paper focuses on a design-consistent regression estimator in which the “auxiliaries” are estimated from a stratified cluster sample and the regression coefficients from an arbitrary subsample of the original sample. The reweighted expansion estimator described in Stukel and Kott (1997) is an example of such an estimator. Assuming that the target variable is a linear function of the auxiliaries plus an error term, asymptotic properties for both this estimator and the jackknife estimator of its mean squared error are developed. These theoretical results are used to explain some of Stukel and Kott’s empirical findings, which in turn shed light on the asymptotic underpinnings of the theoretical results.