In many communication systems training sequences are used to help the receiver identify and/or equalize the channel. The amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization. In this paper we propose the use of a new adaptive filtering method, interior point least squares (IPLS), for adaptive equalization. One of the main features of the algorithm is its fast transient convergence: it thus requires fewer training bits than for example RLS. We apply the IPLS algorithm to update the weight vector for a minimum-mean-square-error decision-feedback equalizer (MMSE-DFE)in a CDMA downlink scenario. Numerical simulations show that when training sequences are short IPLS consistently outperforms RLS in terms of system bit-error-rate. As the training sequence gets longer IPLS matches the performance of the RLS algorithm.