To find the highest tolerable dose of stereotactic hypofractionated radioablation (HYDRA) radiation that can be given to patients with laryngeal cancer. The safety of this radiation will also be studied.

Study Groups:

If participant is found to be eligible to take part in this study, participant will be assigned to a radiation level of HYDRA radiation based on when participant joins this study. Up to 5 dose levels of HYDRA radiation will be tested. Up to 10 participants will be enrolled at each dose level. The first group of participants will receive the lowest dose level. Each new group will receive a higher dose than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of HYDRA radiation is found.

HYDRA Radiation Administration:

If participant is found to be eligible to take part in this study, participant will receive HYDRA radiation on up to 5 days over the course of about 2 weeks.

During radiation, participant will be asked to lie still for about 30-45 minutes. To help make sure that participant's head and neck do not move, participant will wear a head and neck mask. Participant will then have CT or PET-CT scans to make sure that participant is in the right position before participant begins HYDRA radiation. The actual HYDRA radiation treatment will take about 5-10 minutes to complete.

Length of Study Participation:

Participant may continue receiving HYDRA radiation for up to 2 weeks and for a total of 5 times. Participant will no longer be able to receive the study radiation if the disease gets worse, if intolerable side effects occur, or if participant is unable to follow study directions.

Participation on this study will be over after Long-Term Follow-Up. Long-Term Follow-Up may take up to 10 years.

Study Visits:

On Days that participant receives HYDRA:

• Participant will have a speech pathology exam to check participant's voice, swallowing, and breathing function.
• Participant will complete the same 5 questionnaires that participant did at screening.

Follow-Up Visits:

About 6 weeks after participant's last dose of HYDRA radiation:

• Participant will have a physical exam.
• Participant will have a videostroboscopy to check the status of the disease.
• Participant will have a speech pathology exam.
• Participant will have a CT or PET-CT scan to check the status of the disease.
• Participant will complete the same 5 questionnaires that participant did at screening.
• If the doctor thinks it is needed, participant will have a laryngoscopy to check the status of the disease. A laryngoscopy is a standard procedure in which a tube with a lighted camera is inserted through participant's mouth and into participant's throat.
• If the doctor thinks it is needed, participant will have a core biopsy to check the status of the disease. To perform a core biopsy, a sample of tissue is removed using a hollow core needle that has a cutting edge.

About 3 months after participant's last dose of HYDRA radiation:

• Participant will have a physical exam.
• Participant will have a modified barium swallow to test participant's swallowing function and to check the status of the disease.
• Participant will have a CT or PET-CT scan to check the status of the disease.
• Participant will complete the same 5 questionnaires that participant did at screening.
• If the doctor thinks it is needed, participant will have a laryngoscopy to check the status of the disease.
• If the doctor thinks it is needed, participant will have a core biopsy to check the status of the disease.

About 6 months after participant's last dose of HYDRA radiation:

• Participant will have a physical exam.
• Participant will have a videostroboscopy to check the status of the disease.
• Participant will complete the same 5 questionnaires that participant did at screening.
• If the doctor thinks it is needed, participant will have a CT or PET-CT scan to check the status of the disease.
• If the doctor thinks it is needed, participant will have a speech pathology exam.
• If the doctor thinks it is needed, participant will have a laryngoscopy to check the status of the disease.
• If the doctor thinks it is needed, participant will have a core biopsy to check the status of the disease.

Long-Term Follow-Up:

After participant's 6 month follow-up visit, every 3 months for the first 2 years, and then every 6 months after that for up to 5 years:

• Participant will have a physical exam.
• Participant will have a videostroboscopy to check the status of the disease.
• Participant will have a speech pathology exam.
• Participant will have a modified barium swallow to test participant's swallowing function and to check the status of the disease. This will only be done between 3-6 months and then 18-24 months after the first HYDRA dose.
• Participant will complete the same 5 questionnaires that participant did at screening.
• If the doctor thinks it is needed, participant will have a CT or PET-CT scan to check the status of the disease.
• If the doctor thinks it is needed, participant will have a laryngoscopy to check the status of the disease.
• If the doctor thinks it is needed, participant will have a core biopsy to check the status of the disease.

This is an investigational study. HYDRA radiation is delivered using methods that are not FDA-approved or commercially available. It is currently being used for research purposes only. The study doctor can explain how the radiation is designed to work.

Up to 50 participants will be enrolled in this study. All will take part at MD Anderson.

Inclusion Criteria:

1. Patients older than 18 years of age with histologically proven squamous cell carcinoma of the larynx.
2. Stage T1N1/T2-4aN0-1 disease, as defined by American Joint Committee on Cancer (AJCC) criteria.
3. ECOG (Zubrod) performance status 0-2.
4. Must be functionally and technically fit for partial laryngectomy. Subsite study candidates will be evaluated by enrolling physician. The assessment checklist will be submitted at time of enrollment and evaluated by Dr. Gross or Dr. Phan.
5. Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 90 days following completion of therapy. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately.
6. A female of child-bearing potential is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: *Has not undergone a hysterectomy or bilateral oophorectomy; or *Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months).
7. Ability to understand English language and the willingness to sign a written informed consent.

Exclusion Criteria:

1. Patients who have undergone resection of primary disease.
2. Patients who have received induction chemotherapy for their cancer diagnosis.
3. Patients who have undergone a diverting tracheostomy which is either a) traversing directly through tumor, b) has been placed for true airway insufficiency. Patients with a tracheostomy placed preemptively for impending airway compromise remain eligible for enrollment.
4. Prior cancer diagnosis, except appropriately treated localized epithelial skin cancer or cervical cancer.
5. Prior radiation therapy to the head and neck region.
6. Women of childbearing potential (a woman of child-bearing potential is a reproductively mature woman who has not undergone a hysterectomy or who has not been naturally postmenopausal for at least 24 consecutive months [i.e., who has had menses at any time in the preceding 24 consecutive months]) and male participants must practice effective contraception (oral, injectable, or implantable hormonal contraceptive; tubal ligation; intra-uterine device; barrier contraceptive with spermicide; or vasectomized partner) throughout the study.
7. Patients unable or unwilling to give written, informed consent.
8. Severe, active co-morbidity, defined as follows: a. Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months. b. Transmural myocardial infarction within the last 6 months. c. Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration. d. Chronic Obstructive Pulmonary Disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy within 30 days before registration. e. Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects; note, however, that laboratory tests for liver function and f. Acquired Immune Deficiency Syndrome (AIDS) based upon current CDC definition; note, however, that HIV testing is not required for entry into this protocol. Protocol-specific requirements may also exclude immuno-compromised patients.
9. Exclusion #8 continued: g. History of treatment with potent immunosuppressive drugs for such conditions as post organ transplant, severe rheumatoid arthritis, etc. within the past 6 months.
10. Subjects must not be pregnant or nursing due to the potential for congenital abnormalities and the potential of this regimen to harm nursing infants
11. Evidence of metastatic disease