This study will evaluate the effectiveness of the male hormone dehydroepiandrosterone (DHEA) in treating Sjogren's syndrome. This autoimmune disorder, in which the immune system attacks the salivary glands and tear glands, affects primarily women. Patients' eyes and mouth become drier over time, and can lead to problems such as serious tooth decay and eye irritations. Sex hormones seem to influence the immune response and may help decrease disease severity. DHEA has benefited some patients with two other autoimmune diseases, rheumatoid arthritis and systemic lupus erythematosus.