A physcial database system design should take account of skewed block access distributions, nonuniformly distributed attribute domains, and dependent attributes. In this paper we drive general formulas for the number of blocks accessed under these assumptions by considering a class of related occupancy problems. We then proceed to develop robust and accurate approximations for these formulas. We investigate three classes of approximation methods, respectively based on generating functions, Taylor series expansions, and majorization. These approximations are simple to use and more accurate than the cost estimate formulas generated by making uniformity and independence assumptions. Thus they are more representative of the actual database environment, and can be utilized by a query optimizer for better performance.