Testing the Safety of Giving a Standard Dose of Radiation Over a Shorter Period of Time for Patients Who Had Surgery for Intermediate-Risk Head and Neck Cancer

Inclusion Criteria: * Pathologically (histologically) proven diagnosis of squamous cell carcinoma (including variants such as verrucous carcinoma, spindle cell carcinoma, carcinoma NOS, etc.) of the head/neck (oral cavity, oropharynx or larynx); Note: Hypopharynx primaries are excluded because these patients have both a poor prognosis and high likelihood of post- radiation complications. * Clinical stage I-IVA squamous cell carcinoma of the oral cavity, oropharynx or larynx (AJCC 8th edition), including no distant metastases. * General history and physical examination prior to registration; * Chest X-ray (at a minimum) or chest CT scan (with or without contrast) or PET/CT of chest (with or without contrast) prior to registration. * Total resection of the patient's cancer (i.e. no residual disease after total resection of the patient's cancer). * One or more indications for postoperative radiotherapy, based upon pathologic findings: * Perineural invasion; * Lymphovascular invasion; * Single lymph node ≥ 3 cm or ≥ 2 lymph nodes (no extracapsular Extension); * Close margin(s) of resection (close margins defined as cancer extending to within 5 mm of a surgical margin); * Pathologically confirmed T3 or T4a primary tumor; * T2 oral cavity cancer with ≥ 5 mm depth of invasion. * Zubrod Performance Status 0-1. * Age 18-80. * Negative pregnancy test within 14 days prior to registration for participants who may become pregnant. * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety assessment of the investigational regimen are eligible for this trial. * The patient or a legally authorized representative must provide study-specific informed consent prior to study entry. Exclusion Criteria: * Recurrence of the study cancer. * History of systemic lupus erythematosus or systemic sclerosis (scleroderma). * Pregnancy and individuals unwilling to discontinue nursing. * Reliant on a feeding tube (gastric or jejuno) to maintain adequate nutrition at the time of registration * Anticipated need for high-dose systemic chemotherapy (e.g., high dose q3-week cisplatin), multiple systemic therapy agents or immunotherapy. Weekly single-agent systemic therapy with cisplatin, carboplatin, or cetuximab is allowable. * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields; prior chemotherapy for study cancer is not allowed. * Per the operative and/or pathology report, positive margin(s) \[defined as tumor present at the cut or inked edge of the tumor\], nodal extracapsular extension, and/or gross residual disease after surgery; Note: Patients whose tumors had focally positive margins in the main specimen but negative margins from re-excised samples in the region of the positive margin are eligible.