Experimental studies have linked alternans, an abnormal beat-to-beat alternation of cardiac action potential duration, to the genesis of lethal arrhythmias such as ventricular fibrillation. Prior studies have considered various closed-loop feedback control algorithms for perturbing interstimulus intervals in such a way that alternans is suppressed. However, some experimental cases are restricted in that the controller's stimuli must preempt those of the existing waves that are propagating in the tissue, and therefore only shortening perturbations to the underlying pacing are allowed. We present results demonstrating that a technique known as extended time-delay autosynchronization (ETDAS) can effectively control alternans locally while operating within the above constraints. We show that ETDAS, which has already been used to control chaos in physical systems, has numerous advantages over previously proposed alternans control schemes.