The present invention teaches a way of inducing a broad recognition of dominant and subdominant responses to epitopes of any given antigen of importance for prophylaxis or treatment of a chronic disease by immunizing with pools of overlapping 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 primed to include not only the immunodominant epitope recognized when the intact molecule is used for immunization and induced by the chronic infection itself, but induce a much broader and balanced response to a number of the subdominant epitopes as well. The resulting T-cell response to subdominant epitopes is important for protection against chronic diseases that on their own induces a response focused only towards immunodominant epitopes. The present invention requires no prior knowledge of the precise localisation and identity of the subdominant epitopes and their recognition in a human population, but expands the T-cell repertoire and thereby the total number of epitopes recognized by specific T cells primed by vaccination from a few immunodominant epitopes to multiple of epitopes of vaccine relevance. For chronic disease controlled by humoral immunity the T helper cell response primed by the peptide mix may be boosted by the full size protein for maximum induction of an antibody response as well.