This invention provides a method of generating antigen specific allospecific human suppressor CD8+CD28− T cells. This invention also provides a method of generating xenospecific human suppressor CD8+CD28− T cells. This invention further provides a method of generating allopeptide antigen specific human suppressor CD8+CD28− T cells. Methods of treatment for reduction of risk of rejection of allografts and xenografts and autoimmune diseases using the human suppressor CD8+CD28− T cells so produced are also provides, as are methods of preventing rejection and autoimmune diseases, and vaccines comprising the produced suppressor T cells. Methods of diagnosis to determine whether a level of immuno-suppressant therapy requires a reduction are provided.