A single-celled amoeba can solve the traveling salesman problem through its shape-changing dynamics. In this paper, we examine roles of several elements in a previously proposed computational model of the solution-search process of amoeba and three modifications towards enhancing the solution-search preformance. We find that appropriate modifications can indeed significantly improve the quality of solutions. It is also found that a condition associated with the volume conservation can also be modified in contrast to the naive belief that it is indispensable for the solution-search ability of amoeba. A proposed modified model shows much better performance.