The objective of this study is to assess the safety and efficacy of an immunosuppression-minimizing regimen consisting initially of Thymoglobulin induction in combination with tacrolimus, mycophenolate mofetil, and rapid steroid withdrawal. The protocol will minimize long-term calcineurin inhibitor exposure and toxicity by weaning tacrolimus starting at 3 months after transplantation. Patients will be eligible to participate in this study only if they have already consented to participate in another study entitled "The use of urinary PCR test to help detect rejection in kidney transplant patients". In "The use of urinary PCR test to help detect rejection in kidney transplant patients", kidney allograft status (ie. whether or not there is any immunologic activity in the transplant kidney)is characterized with the use of protocol biopsies, diagnostic biopsies, and urinary PCR profiles. At 3 months after transplant, these patients are on an immunosuppression regimen consisting of tacrolimus (Prograf) and mycophenolate mofetil (CellCept). Prograf dosing is managed through the measurement of trough levels. For the first 3 months after transplant, patients are maintained at a trough level between 8 to 10 ng/ml. After 3 months, this target level is lowered in order to minimize long-term exposure to immunosuppressive agents. However, there is no consensus as to what the proper level should be after the first 3 months. Therefore, this study will randomize patients to 2 groups, one group will have their trough level targeted between 6 to 8 ng/mL while the other group will have their trough targeted between 3 and 5 ng/mL. By doing this study, we hope to determine which trough level is best, both for protecting the patient from rejection and protecting the patient from the adverse effects of the immunosuppressive medications.