The invention describes the development of more potent peptide vaccines to prevent or treat infections or cancer and their administration to a subject in order to elicit a T cell response in the subject. Small synthetic peptides from the known sequences of viral, bacterial, parasitic or tumor antigens are modified so they can spontaneously form complexes with a synthetic nucleic acid, such as Poly IC, that functions as an immunological adjuvant. The peptide-nucleic acid complexes are dramatically more immunogenic as compared to the separate components. The procedure for developing the vaccine involves the conjugation of a synthetic peptide containing a C residue to poly-K using a bi-functional cross-linking reagent (SMCC). The peptide/poly-K complex was then formulated with CMC and poly-IC to produce a self-adjuvant vaccine that was 36-fold more effective as compared to the same peptide administered mixed with the same adjuvant (but not complexed to it).