We propose and evaluate two indexing schemes for improving the efficiency of data retrieval in high-dimensional databases that are incomplete. These schemes are novel in that the search keys may contain missing attribute values. The first is a multi-dimensional index structure, called the Bitstring-augmented R-tree (BR-tree), whereas the second comprises a family of multiple one-dimensional one-attribute (MOSAIC) indexes. Our results show that both schemes can be superior over exhaustive search. Experimental results suggest that BRtrees have lower update and storage costs and are able to support range queries more efficiently under most circumstances, when compared to the MOSAIC indexing scheme. However, contrary to conventional wisdom, the MOSAIC structure outperforms the BR-tree in retrieval time for point queries, as well as in range queries over incomplete databases for dimension-unrestricted data distributions.