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 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.