Abstract: Contemporary database technology is severely limited at managing high-dimensional data of many advanced applications, such as multimedia systems and data mining. The main concern of this paper is the well-known performance degradation of multi-dimensional access methods in spaces with many dimensions. The paper proposes an elaborate storage organization, called the inverted space, which can support efficient processing of data in spaces with very high dimensionality. The organization allows system administrators to control the size of spatial indexes and, thereby, avoid the negative impact of extremely high data dimensionality on the retrieval performance. In addition, the paper introduces a new point access method designed to address numerous other problems that the contemporary retrieval schemes experience in high-dimensional situations. This mechanism is envisioned to serve as the core indexing structure of the inverted-space storage organizations.