This is a randomized Phase III study comparing two doses of definitive radiation therapy given with induction and concurrent chemotherapy in HPV-positive oropharynx, unknown primary or nasopharynx cancer. Eligible, consented and registered patients will receive three cycles of Docetaxel Cisplatin and 5-FU (TPF) induction chemotherapy. After 3 cycles, the patients will be assessed for clinical, radiographic and pathologic response to TPF. Patients with a clinical or radiographic CR or PR will be randomized on the second phase of this study, where patients will undergo a 2:1 randomization to reduced (5600 cGy) or standard (7000 cGy) dose radiotherapy with weekly Carboplatin. Patients not meeting the response criteria will be treated with standard dose CRT. Patients not completing 3 cycles TPF for reasons of toxicity, progressive disease, choice, or other medical necessity will be treated with standard dose CRT or surgery depending on their primary site and overall medical condition and followed for survival. Toxicity will be assessed by Symptom scores, QOL and SAE monitoring. The primary end point of the trial is equivalent local regional control and PFS at 3 years. Patients will be followed for 5 years.