Combinatorial interaction testing is a well-studied testing strategy that aims at constructing an effective interaction test suite (ITS) of a specific generation strength to identify interaction faults caused by the interactions among factors. Due to limited testing resources in practice, for example in combinatorial interaction regression testing, interaction test suite prioritization (ITSP) has been proposed to improve the efficiency of testing. An intuitive ITSP strategy that has been widely used in practice is fixed-strength interaction coverage based prioritization (FICBP). FICBP makes use of a property of the ITS: interaction coverage at a fixed prioritization strength. However, a challenge facing FICBP is that, when the ITS is large, the prioritization cost can be very high. In this paper, we propose a new FICBP method that, by repeatedly using base choice coverage (i.e., one-wise coverage) during the prioritization process, improves testing efficiency while maintaining testing effectiveness. The empirical studies show that our method has fault detection capability comparable to current FICBP methods, but obtains more stable results in many cases. Additionally, our method requires considerably less prioritization time than other FICBP methods at different prioritization strengths.