The importance of dominance and skyline analysis has been well recognized in multi-criteria decision making applications. Most previous studies assume a fixed order on the attributes. In practice, different customers may have different preferences on nominal attributes. In this paper, we identify an interesting data mining problem, finding favorable facets, which has not been studied before. Given a set of points in a multidimensional space, for a specific target point p we want to discover with respect to which combinations of orders (e.g., customer preferences) on the nominal attributes p is not dominated by any other points. Such combinations are called the favorable facets of p. We consider both the effectiveness and the efficiency of the mining. A given point may have many favorable facets. We propose the notion of minimal disqualifying condition (MDC) which is effective in summarizing favorable facets. We develop efficient algorithms for favorable facet mining for different application scenarios. The first method computes favorable facets on the y. The second method pre-computes all minimal disqualifying conditions so that the favorable facets can be looked up in constant time. An extensive performance study using both synthetic and real data sets is reported to verify their effectiveness and efficiency.