The synchronous interference cancellation problem is addressed when training and working intervals are available that contain the desired signal and completely overlapping interference. A maximum-likelihood (ML) approach is applied for estimation of the structured covariance matrices over both training and working intervals for a Gaussian data model. It is shown that the efficiency of the ML solution is close to the efficiency of the least-squares (LS) estimator, which means that the conventional training-based LS algorithm practically cannot be improved upon in the class of second-order semiblind techniques under the synchronous interference scenario.