Vaccine Therapy in Treating HLA-A2 Positive Patients With Melanoma

Inclusion Criteria: * Patients must have histologically confirmed primary melanoma of Breslow thickness 1.0-4.0 mm; patients who have had only their initial biopsy are preferred; however, those who have already undergone a wide local excision are also eligible; patients may be enrolled up to three months after their wide local excision * Patients whose melanoma is \> 4.0 mm thick who have positive or negative regional lymph nodes are also eligible * After accrual to the original 26 patient goal, all patients must be enrolled prior to sentinel lymph node dissection; patients with previous lymph node dissection will not be eligible * Patients must be HLA typed and be shown to be HLA-A2.1+ by either serologic techniques, flow cytometry, or molecular techniques * Patients must be ambulatory with good performance status (Karnofsky performance status \[PS\] 80-100) * White blood cell (WBC) \>= 3500/mm\^3 * Platelets (Plt) \>= 100,000/mm\^3 * Hemoglobin \>= 9 gm/100 ml * Serum creatinine =\< 2 mg/dl * Total bilirubin =\< 2.0 mg/dl * Patients must have recovered from any effects of major surgery and be free of significant systemic infection * Patients must be negative for human immunodeficiency virus (HIV) antibody by enzyme-linked immunosorbent assay (ELISA) (or negative by Western blot if ELISA is positive) if they are considered to be at high risk; others do not require serologic testing if there are no symptoms or risk factors for HIV disease * Women of childbearing potential mu…