Latent Semantic Indexing (LSI) is commonly used to match queries to documents in information retrieval applications. LSI has been shown to improve retrieval performance for some, but not all, collections, when compared to traditional vector space retrieval. In this paper, we first develop a model for understanding which values in the reduced dimensional space contain the term relationship (latent semantic) information. We then test this model by developing a modified version of LSI that captures this information, Essential Dimensions of LSI (EDLSI). EDLSI significantly improves retrieval performance on corpora that previously did not benefit from LSI, and offers improved runtime performance when compared with traditional LSI. Traditional LSI requires the use of a dimensionality reduction parameter which must be tuned for each collection. Applying our model, we have also shown that a small, fixed dimensionality reduction parameter (k=10) can be used to capture the term relationship information in a corpus.