This phase II trial studies how well lower-dose chemotherapy plus radiation (chemoradiation) therapy works in comparison to standard-dose chemoradiation in treating patients with early-stage anal cancer. Drugs used in chemotherapy, such as mitomycin, fluorouracil, and capecitabine, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Radiation therapy uses high-energy x-rays to kill tumor cells and shrink tumors. Giving chemotherapy with radiation therapy may kill more tumor cells. This study may help doctors find out if lower-dose chemoradiation is as effective and has fewer side effects than standard-dose chemoradiation, which is the usual approach for treatment of this cancer type.