In this paper we extend previous work on using bintrees as an efficient representation for qualitative information about spatial objects. Our approach represents each spatial object as a bintree satisfying the exact same qualitative relationships to other bintree representations as the corresponding spatial objects. We prove that such correct bintrees always exists and that they can be constructed as a sum of local representations, allowing a practically efficient construction. Our representation is both efficient, w.r.t. storage space and query time, and can represent many well-known qualitative relations, such as the relations in the Region Connection Calculus and Allen's Interval Algebra.