The present invention teaches a convenient way of inducing a broad recognitionof dominant and subdominant responses to epitopes of any given antigen of importancefor prophylaxis or treatment of a chronic disease by immunizing with pools ofoverlapping fragments (synthetic peptides e.g. 10-30 mers with 2-20 aa overlap)of the desired antigen in appropriate adjuvants. The T cell repertoire is primedto include not only the immunodominant epitope recognized when the intact moleculeis used for immunization and induced by the chronic infection itself, but inducea much broader and balanced response to a number of the subdominant epitopes aswell. The resulting T-cell response to subdominant epitopes is important forprotection against chronic diseases that on their own induces a response focusedonly towards immunodominant epitopes. The major advantage of the present inventionis that it requires no prior knowledge of the precise localisation and identityof the subdominant epitopes and their recognition in a human population, butexpands the T-cell repertoire and thereby the total number of epitopes recognizedby specific T cells primed by vaccination from a few immunodominant epitopesto multiple of epitopes of vaccine relevance. For chronic disease controlledby humoral immunity the T helper cell response primed by the peptide mix may convenientlybe boosted by the full size protein for maximum induction of an antibody responseas well.