A physical database system design should take account of skewed block access distributions, nonuniformly distributed attribute domains, and dependent attributes. In this paper we derive 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 clases of approximation methods, respectively based on generating functions, Taylor series expansions, and majorization. These approximations are as simple to use and far more accurate than the cost estimate formulas generated by making independence and uniformity assumptions.