We consider the problem of answering a series of on-line queries on a static data set. The conventional approach to such problems involves a preprocessing phase which constructs a data-structure with good search behavior. The data structure representing the data set then remains fixed throughout the processing of the queries. Our approach involves dynamic or query-driven structuring of the data set; our algorithm processes the data set only when doing so is required for answering a query. A data structure constructed progressively in this fashion is called a deferred data structure. We develop the notion of deferred data structures by solving the problem of answering membership queries on an ordered set. We obtain a randomized algorithm which achieves asymptotically optimal performance with high probability. We then present optimal deferred data structures for the following problems in the plane: testing convex-hull membership, half- plane intersection queries and fixed-constraint multi-objective linear programming. We also apply the deferred data structuring technique to multi-dimensional dominance query problems.