In preceding papers [8], [11], [12], [6], a class of matrices (-matrices) has been developed which are data-sparse and allow to approximate integral and more general nonlocal operators with almost linear complexity. In the present paper, a weaker admissibility condition is described which leads to a coarser partitioning of the hierarchical -matrix format. A coarser format yields smaller constants in the work and storage estimates and thus leads to a lower complexity of the -matrix arithmetic. On the other hand, it preserves the approximation power which is known in the case of the standard admissibility criterion. Furthermore, the new weak -matrix format allows to analyse the accuracy of the -matrix inversion and multiplication.