Combination Chemotherapy Followed by Radiation Therapy in Treating Young Patients With Newly Diagnosed Hodgkin's Lymphoma

Inclusion Criteria:

* Histologically confirmed Hodgkin's lymphoma meeting the following criteria:

  * Newly diagnosed disease
  * Stage IA OR stage IIA without bulky disease
  * No lymphocyte-predominant histology
* Staging on this study will be determined by the clinical stage; surgical staging is strongly discouraged, except for the rare situation of equivocal imaging studies below the diaphragm
* Patients may not have received any previous chemotherapy or radiation therapy; patients may not have received systemic corticosteroids within 30 days of enrollment on this protocol; steroids used for treatment of contrast agent allergy required for computed tomography (CT) scans are acceptable
* Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^3
* Total bilirubin =\< 1.5 x normal
* Alanine (ALT) =\< 2.5 x normal
* Shortening fraction \>= 27% by echocardiogram OR ejection fraction \>= 50% by multi-gated acquisition (MUGA)
* No pathologic prolongation of QTc interval on 12-lead electrocardiography (ECG)
* Female patients of childbearing potential must have a negative pregnancy test
* Lactating females must agree that they will not breastfeed a child while on this study
* Fertile patients must use effective contraception
* Males and females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method
* All patients and/or their parents or legal guardians must sign a written informed consent
* All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met