We address the problem of skyline query processing for a count-based window of continuous streaming data that involves both totally- and partially-ordered attribute domains. In this problem, a fixedsize buffer of the N most recent tuples is dynamically maintained and the key challenge is how to efficiently maintain the skyline of the sliding window of N tuples as new tuples arrive and old tuples expire. We identify the limitations of the state-of-the-art approach STARS, and propose two new approaches, STARS+ and SkyGrid, to address its drawbacks. STARS+ is an enhancement of STARS with three new optimization techniques, while SkyGrid is a simplification STARS that eliminates a key data structure used in STARS. While both new approaches outperform STARS significantly, the surprising result is that the best approach turns out to be the simplest approach, SkyGrid.