Participation in this study will be determined by how well patients tolerate the assigned regimen and by how their disease responds. Patients will continue taking their assigned regimen for 6 months as long as it is felt that their disease is stable (based on their PSA levels) and they are tolerating the treatment. After 6 months or earlier, if the disease progresses, the treatment code will be broken. If patients were on celecoxib, they will be taken off study. The patient's doctor will discuss other available treatment options with him/her at that time, including continuing celecoxib "off study". If patients were on placebo, they will then have the option to begin taking celecoxib. If patients start celecoxib treatment, they will be treated in this study with celecoxib for 6 months or until their disease progresses. After 6 months on celecoxib or sooner, if their disease progresses, they will be taken off study. The patient's doctor will discuss available treatment options with him/her at that time, including continuing celecoxib "off study".