A method for identifying T-cell epitopes which can be used to elicit T cells targeting cells capable of regenerating cancers is disclosed. The method identifies T-cell epitopes with a high curative potential, high potency and high probability of T cell recognition (HP). The method includes: (i) identifying high curative potential tumor protein target i.e., identifying HP-TP; (ii) identifying peptide sequences within the protein sequence of an HP-TP that have a high probability of eliciting T cell killing; and (iii) qualifying the sequence specificity based on the fold difference between the specific target and non-targets. The identified T-cell epitopes include a core sequence of 9 amino acids homologous to a sequence expressed within a qualified HP-TP. The T-cell epitopes can be used in a method for reprograming T cells to selectively attack tumor cells capable of perpetuating a tumor and treating patients, for example, cancer patients.