The present invention provides a method of carrying out adoptive immunotherapy in a primate subject in need thereof by administering the subject a cytotoxic T lymphocytes (CTL) preparation in a treatment-effective amount. The method comprises administering as the CTL preparation a preparation consisting essentially of an in vitro expanded primate CTL population, the CTL population enriched prior to expansion for central memory T lymphocytes, and depleted prior to expansion of effector memory T lymphocytes. In some embodiments, the method may further comprise concurrently administering Interleukin-15 to the subject in an amount effective to increase the proliferation of the central memory T cells in the subject. Pharmaceutical formulations produced by the method, and methods of using the same, are also described.