Skyline queries are useful in many applications such as multi-criteria decision making, data mining, and user preference queries. A skyline query returns a set of interesting data objects that are not dominated in all dimensions by any other objects. For a high-dimensional database, sometimes it returns too many data objects to analyze intensively. To reduce the number of returned objects and to find more important and meaningful objects, we consider a problem of k-dominant skyline queries. Given an n-dimensional database, an object p is said to k-dominates another object q if there are dimensions in which p is better than or equal to q. A k-dominant skyline object is an object that is not k-dominated by any other objects. In contrast, conventional skyline objects are n-dominant objects. We propose an efficient method for computing k-dominant skyline queries. Intensive performance study using real and synthetic datasets demonstrated that our method is efficient and scalable.