This phase II clinical trial is studying how well response-based therapy assessed by PET scan works in treating patients with bulky stage I and stage II Hodgkin lymphoma. PET scans will be obtained during the course of therapy. Researchers will evaluate the usefulness of this PET scan to determine whether radiation may be left out in the treatment of disease if the PET scan shows a response to chemotherapy alone. In addition, a small percentage of patients may have disease that is not adequately treated with ABVD (doxorubicin, bleomycin, vinblastine, and dacarbazine) and radiotherapy. Researchers hope to identify this group of patients using early PET scans and will change to a chemotherapy treatment called BEACOPP (bleomycin, etoposide, doxorubicin, cyclophosphamide, vincristine, procarbazine and prednisone).