In comparing two treatments A and B in a clinical trial usually patients from ethical points of view are not assigned to treatment groups by complete randomization. In this paper a general class of assignment rules including the biased coin design, the urn design, and the adaptive biased coin design is considered. Patients are assigned to treatment groups sequentially under restricted randomization. Let \(\eta\) be the limiting proportion of patients assigned to A, where \(01)\) there are m patients in treatment A. Then p(m/n) is the probability that A will be assigned to the \((n+1)th\) patient. Exact and approximate confidence intervals for the treatment differences are derived under this restricted randomization. The interval estimation is illustrated with a real-life example.