Atomic properties are central to discussions of bonding and reactivity, and topological electron density analysis provides a powerful framework for their rigorous determination. Whereas the topological method can be applied routinely to comparatively small molecules, its application to large molecules is somewhat impeded by the rather considerable amounts of computer time required. Here, we describe two new methods for the determination of integrated atomic properties that greatly reduce the integration times while maintaining the generality, the rigor, and the accuracy of the topological partitioning method. The principle of the methods consists in reducing the total molecular electron density function to atom-specific electron density functions that accurately describe the electron density distribution in the basin of the atom whose properties are being determined. It is shown that this task can be accomplished either by a reduction of the space of the primitives in which the wave function is expanded or via electron density functions defined by atom-specific subsets of selected localized molecular orbitais. With the current integration algorithm the latter method is more efficient. The two methods can be combined. The theoretical principles and the computational implementation of the methods are discussed. Their performances have been tested for a series of polyines C2nH2 and polynitriles CnNnHn+2 (n=1-5 and 10) and the topological characteristics and the integrated properties are found to be in excellent agreement with results obtained by the conventional technique. Importantly, it is shown that with the subset selection, integration time requirements approach an upper limit as the size of the molecule increases. The methods perform equally well for all kinds of basis sets, allowing for the analysis of large molecules described by spliced basis sets. The rigorous electron density analysis of very large molecular systems becomes feasible.