  We examine the problem of construction of confidence intervals within the
basic single-parameter, single-iteration variation of the method of
quasi-optimal weights. Two kinds of distortions of such intervals due to
insufficiently large samples are examined, both allowing an analytical
investigation. First, a criterion is developed for validity of the assumption
of asymptotic normality together with a recipe for the corresponding
corrections. Second, a method is derived to take into account the systematic
shift of the confidence interval due to the non-linearity of the theoretical
mean of the weight as a function of the parameter to be estimated. A numerical
example illustrates the two corrections.
