The invention is drawn to compositions and methods for the induction of an immune response, in particular a strong CD8 T cell response, to a specific antigenic determinant without raising a significant antibody response to the antigenic determinant after a first, priming immunization. The method comprises administering to the host a recombinant poxviral vector comprising a transcriptional control element comprising an early and/or late element linked to a nucleotide sequence encoding the antigenic determinant. The recombinant poxviral vector comprises a transcriptional control element comprising an early and/or late element linked to a nucleotide sequence encoding the antigenic determinant. The late element may be stronger than the cowpox ATI promoter in HeLa cells.