Deoxyribonucleic acid (DNA) is a molecule that consists of two complementary sequences of amino acids. Reading these sequences is an important task in biology, called DNA sequencing. However, large DNA molecules cannot be read in one piece. Therefore, existing techniques first break the given DNA molecules up into small fragments which can be read. One of these techniques is called the hybridization experiment. The reconstruction of the original DNA molecule from these fragments is a challenging problem from the computational point of view. In recent years the specific problem of DNA sequencing by hybridization has attracted quite a lot of interest in the optimization community. While most researchers focused on the development of metaheuristic approaches, work on simple constructive heuristics hardly received any attention. This is despite the fact that well-working constructive heuristics are often an essential component of succesful metaheuristics. It is exactly this lack of constructive heuristics that motivated the work presented in this paper. The results of our best constructive heuristic are comparable to the results of the best existing metaheuristics, while using less computational time.