Inclusion Criteria:

   - STEP 1: REGISTRATION

   - Pathologically (histologically or cytologically) proven diagnosis of squamous cell
   carcinoma (including the histological variants papillary squamous cell carcinoma and
   basaloid squamous cell carcinoma) of the oropharynx (tonsil, base of tongue, soft
   palate, or oropharyngeal walls); cytologic diagnosis from a cervical lymph node is
   sufficient in the presence of clinical evidence of a primary tumor in the oropharynx;
   clinical evidence should be documented, may consist of palpation, imaging, or
   endoscopic evaluation, and should be sufficient to estimate the size of the primary
   (for T stage)

   - Patients must have clinically or radiographically evident measurable disease at the
   primary site or at nodal stations; tonsillectomy or local excision of the primary
   without removal of nodal disease is permitted, as is excision removing gross nodal
   disease but with intact primary site; limited neck dissections retrieving =< 4 nodes
   are permitted and considered as non-therapeutic nodal excisions

   - Immunohistochemical staining for p16 must be performed on tissue, and this tissue must
   be submitted for central review; fine needle aspiration (FNA) biopsy specimens may be
   used as the sole diagnostic tissue if formalin-fixed paraffin-embedded cell block
   material is available for p16 immunohistochemistry; FNA specimens prepared with
   adequate p16 testing in this manner are acceptable to submit for central review; if
   the p16 preparation is not adequate, additional specimens will be required to
   establish p16 status; centers are encouraged to contact the pathology chairs for
   clarification

   - Clinical stage T1-T2, N1-N2b or T3, N0-N2b (American Joint Committee on Cancer [AJCC],
   7th edition [ed.]) including no distant metastases based on the following diagnostic
   workup:

      - General history and physical examination within 56 days prior to registration

      - Fiberoptic exam with laryngopharyngoscopy (mirror and/or fiberoptic and/or direct
      procedure) within 70 days prior to registration

      - One of the following combinations of imaging is required within 56 days prior to
      registration:

         - A CT scan of the neck (with contrast) and a chest CT scan (with or without
         contrast)

         - Or a magnetic resonance imaging (MRI) of the neck (with contrast) and a
         chest CT scan (with or without contrast)

         - Or a CT scan of neck (with contrast) and a PET/CT of neck and chest (with or
         without contrast)

         - Or an MRI of the neck (with contrast) and a PET/CT of neck and chest (with
         or without contrast)

            - Note: a CT scan of neck and/or a PET/CT performed for the purpose of
            radiation planning may serve as both staging and planning tools

   - Patients must provide their personal smoking history prior to registration; the
   lifetime cumulative history cannot exceed 10 pack-years; the following formula is used
   to calculate the pack-years during the periods of smoking in the patient's life; the
   cumulative total of the number of pack-years during each period of active smoking is
   the lifetime cumulative history

      - Number of pack-years = (frequency of smoking [number of cigarettes per day] x
      duration of cigarette smoking [years])/20

      - Note: twenty cigarettes is considered equivalent to one pack; the effect of
      non-cigarette tobacco products on the survival of patients with p16-positive
      oropharyngeal cancers is undefined; cigar and pipe tobacco consumption is
      therefore not included in calculating the lifetime pack-years; marijuana
      consumption is likewise not considered in this calculation; there is no clear
      scientific evidence regarding the role of chewing tobacco-containing products in
      this disease; investigators are discouraged from enrolling patients with a
      history of very sustained use (such as several years or more) of non-cigarette
      tobacco products alone

   - Zubrod performance status of 0-1 within 56 days prior to registration

   - Absolute neutrophil count (ANC) >= 1,500 cells/mm^3

   - Platelets >= 100,000 cells/mm^3

   - Hemoglobin >= 8.0 g/dl; Note: the use of transfusion or other intervention to achieve
   hemoglobin (Hgb) >= 8.0 g/dl is acceptable

   - Serum creatinine =< 1.5 mg/dl or creatinine clearance (CC) >= 50 ml/min determined by
   24-hour collection or estimated by Cockcroft-Gault formula

   - Bilirubin =< 2 mg/dl

   - Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =< 3 x the upper
   limit of normal

   - Negative serum pregnancy test within 14 days prior to registration for women of
   childbearing potential

   - Patients who are human immunodeficiency virus (HIV) positive but have no prior
   acquired immune deficiency syndrome (AIDS)-defining illness and have cluster of
   differentiation (CD)4 cells of at least 350/mm^3 are eligible; HIV-positive patients
   must not have multi-drug resistant HIV infection or other concurrent AIDS-defining
   conditions; patients must not be seropositive for hepatitis B (hepatitis B surface
   antigen positive or anti-hepatitis B core antigen positive) or seropositive for
   hepatitis C (anti-hepatitis C antibody positive); however, patients who are immune to
   hepatitis B (anti-hepatitis B surface antibody positive) are eligible (e.g. patients
   immunized against hepatitis B)

   - The patient must provide study-specific informed consent prior to study entry,
   including consent for mandatory submission of tissue for required, central p16 review

   - Patients who speak English (or read one of the languages for which a translation is
   available must consent to complete the mandatory dysphagia-related patient reported
   instrument (MDADI); if the patient cannot understand spoken English and reads only
   languages not available in the MDADI translations, the patient can still participate
   in the trial, as this has been factored into the trial statistics; for all other
   patients, the MDADI is mandatory as it is included in the primary endpoint to be
   studied

   - STEP 2: RANDOMIZATION

   - p16 positive by immunohistochemistry (defined as greater than 70% strong nuclear or
   nuclear and cytoplasmic staining of tumor cells, confirmed by central pathology
   review)

Exclusion Criteria:

   - STEP 1 (REGISTRATION)

   - Cancers considered to be from an oral cavity site (oral tongue, floor mouth, alveolar
   ridge, buccal or lip), or the nasopharynx, hypopharynx, or larynx, even if p16
   positive, or histologies of adenosquamous, verrucous, or spindle cell carcinomas

   - Carcinoma of the neck of unknown primary site origin (even if p16 positive)

   - Radiographically matted nodes, defined as 3 abutting nodes with loss of the
   intervening fat plane

   - Supraclavicular nodes, defined as nodes visualized on the same axial imaging slice as
   the clavicle

   - Definitive clinical or radiologic evidence of metastatic disease or adenopathy below
   the clavicles

   - Gross total excision of both primary and nodal disease with curative intent; this
   includes tonsillectomy, local excision of primary site, and nodal excision that
   removes all clinically and radiographically evident disease; in other words, to
   participate in this protocol, the patient must have clinically or radiographically
   evident gross disease for which disease response can be assessed

   - Patients with simultaneous primary cancers or separate bilateral primary tumor sites
   are excluded with the exception of patients with bilateral tonsil cancers

   - Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free
   for a minimum of 1095 days (3 years) (for example, carcinoma in situ of the breast,
   oral cavity, or cervix are all permissible)

   - Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a
   different cancer is allowable

   - Prior radiotherapy to the region of the study cancer that would result in overlap of
   radiation therapy fields

   - Severe, active co-morbidity defined as follows:

      - Unstable angina and/or congestive heart failure requiring hospitalization within
      the last 6 months

      - Transmural myocardial infarction within the last 6 months

      - Acute bacterial or fungal infection requiring intravenous antibiotics at the time
      of registration

      - Chronic obstructive pulmonary disease exacerbation or other respiratory illness
      requiring hospitalization or precluding study therapy within 30 days of
      registration

      - Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects;
      note, however, that laboratory tests for liver function and coagulation
      parameters are not required for entry into this protocol other than those
      requested

      - Acquired immune deficiency syndrome (AIDS) based upon current Centers for Disease
      Control and Prevention (CDC) definition; note, however, that HIV testing is not
      required for entry into this protocol; protocol-specific requirements may also
      exclude immuno-compromised patients

   - Pregnancy

   - Prior allergic reaction to cisplatin