Supervisory control of discrete event systems using limited lookahead has been studied by Chung-Lafortune-Lin, where control is computed by truncating the plant behavior up to the limited lookahead window. We present a modification of this approach in which the control is computed by extending the plant behavior by arbitrary traces beyond the limited lookahead window. The proposed supervisor avoids the notion of pending traces. Consequently the need for considering either a conservative or an optimistic attitude regarding pending traces (as in the work of Chung-Lafortune-Lin) does not arise. It was shown that an optimistic attitude may result in violation of the desired specifications. We demonstrate here that a conservative attitude may result in a restrictive control policy by showing that in general the proposed supervisor is less restrictive than the conservative attitude based supervisor. Moreover, the proposed approach uses the notion of relative closure to construct the supervisor so that it is non-blocking even when the desired behavior is not relative closed (Chung-Lafortune-Lin assume relative closure). Finally, the proposed supervisor possesses all the desirable properties that a conservative attitude based supervisor of Chung-Lafortune-Lin possesses. We illustrate our approach by applying it to concurrency control in database management systems.