The goal of this clinical research study is to compare the use of MRI simulations to plan different doses of intensity modulated radiotherapy (IMRT) to the standard IMRT dose in patients with low risk human papilloma virus positive oropharyngeal cancer. This is an investigational study. MRI simulations and radiation therapy are delivered using FDA-approved and commercially available methods. The use of MRI imaging to plan the dose is investigational. Up to 90 participants will be enrolled in this study. All will take part at MD Anderson.

Baseline Visit: If you are found to be eligible to take part in this study and agree, you will have a baseline visit. The following tests and procedures will be performed: * You will have a hearing test. * You will have a dental exam. During this exam, your saliva flow will be measured and you will be checked for lockjaw. * Your swallowing function will be tested with a special type of x-ray called a modified barium swallow (MBS). During the test, you will eat and drink foods and liquids mixed with a "contrast" chemical called barium that will make your throat more visible in the x-rays. A special x-ray tube will be connected to a television screen to allow the doctor to watch the foods and liquids pass from your mouth and down your throat. * You will complete a questionnaire about swallowing that should take about 5 minutes to complete. * You will have a video-strobe procedure to check your vocal cords. To perform a video-strobe procedure, a small camera will be inserted into the throat through your nose or mouth. You will be awake for this procedure and the study staff will give you the option of receiving a numbing spray for your nose and/or throat. * Photos of the inside of your mouth will be taken to check for mouth sores. * You will fill out questionnaires about your quality of life, work status, medical history, smoking status, and any symptoms you may have. Completing these questionnaires should take about 10-15 minutes. Study Groups: If you are among the first 15 patients enrolled in the study, you will be in Group 1. If you join the study after the first 15 patients have enrolled, you will be randomly assigned (as a flip of a coin) to 1 of 2 study groups. This is done because no one knows if one study group is better, the same, or worse than the other group. * If you are in Group 1, an MRI will be used to plan your IMRT. * If you are in Group 2, you will receive standard-of-care IMRT. Length of Study Participation: No matter which group you are in, you may continue receiving radiation therapy for up to 6 ½ weeks. You will no longer be able to take part in this study if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions. Your overall participation on the study will be over after 5 years. Treatment Planning and Schedule: You will receive a standard CT simulation which will cover your head and neck for treatment planning. You will also have a PET-CT to check the status of the disease and for treatment planning purposes. If you are among the first 15 participants or are in Group 1, you also will have an MRI simulation for treatment planning purposes. All groups will then receive radiation therapy 1 time each day, 5 days a week (Monday through Friday) for up to 33 treatments (about 6 ½ weeks). Study Visits: Every week while you are receiving radiation therapy: * You will have a physical exam. * Blood (about 1-2 tablespoons) will be drawn for routine tests. * You will fill out the same questionnaires as before. * You will have an MRI. At Weeks 3 and 6: * Photos of the inside of your mouth will be taken to check for mouth sores. * You will have a dental exam. If you are among the first 15 participants or are in Group 1, you will also have the MRI simulation at the end of Weeks 1, 2, 3, and 4 of treatment. Six (6) weeks after finishing radiation therapy, you will complete the same questionnaires as before. Within 8-12 weeks after finishing radiation therapy: * Photos of the inside of your mouth will be taken to check for mouth sores. * You will have a hearing test. * If you are among the first 15 participants or are in Group 1, you will have an MRI simulation. Six (6) months, 1 year, and 2 years after finishing radiation therapy: * You will fill out the same questionnaires as before. * You will have a mouth exam to check your swallowing function. * Photos of the inside of your mouth will be taken to check for mouth sores. * You will fill out the same questionnaires as before. * You will have a video-strobe procedure to check your vocal cords. * At 1 year only, you will have a dental exam and an MBS exam to test your swallowing function. * At 1 year and 2 years only, you will also have a hearing test. Three to six (3-6) months, 1 year, and 18-24 months after finishing radiation therapy: * You will have an MBS exam to test your swallowing function. * You will fill out the same questionnaires as before. * You will have the video-strobe procedure to check your vocal cords. Two (2) years after finishing radiation therapy and if the disease gets worse, blood (about 3 teaspoons) will be drawn for circulating tumor cells (CTCs). This is a test of how many tumor cells are in the blood. Five (5) years after finishing radiation therapy, you will have an MBS exam to test your swallowing function and will complete the same questionnaires as before. If the doctor thinks it is needed during follow-up, you will have a tumor biopsy for tumor marker testing and a CT scan, MRI scan and/or PET/CT scan to check the status of the disease. Follow-Up Calls: During the 8-12 weeks while you are recovering from treatment, you will be called or emailed by an automated system every 2 weeks. This will be to remind you to fill out a web-based form that asks about any side effects you may have had. Completing the form should take about 10-15 minutes each time.