For Finite State Machine (FSM) based testing, it has been shown that the use of shorter Adaptive Distinguishing Sequences (ads) yields shorter test sequences. It is also known, on the other hand, that constructing a minimum cost ADS is an NP-hard problem and it is NP-hard to approximate. In this paper, we introduce a lookahead-based greedy algorithm to construct reduced ADSs for FSMs. The greedy algorithm inspects a search space to make a decision. The size of the search space is adjustable, allowing a trade-off between the quality and the computation time. We analyse the performance of the approach on randomly generated FSMs by comparing the ADSs constructed by our algorithm with the ADSs that are computed by the existing algorithms.