A convenient 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 is provided. The method involves 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 vaccination with peptide mix induces a T-cell response that includes response to subdominant epitopes is important for protection against chronic disease that on their own induces a response focused only on immunodominant epitopes. The major advantage of the present invention is that it requires no prior knowledge of the precise localization 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 a multiple of epitopes.