Total Thyroidectomy With and Without Prophylactic Central Neck Lymph Node Dissection in People With Low-risk Papillary Thyroid Cancer

Background: \- Papillary thyroid cancer (PTC) often spreads to lymph nodes in the neck. This can be hard to detect. People often have lymph nodes removed anyway, and researchers want to study if this is a good idea. Objective: \- To compare the effectiveness of removing lymph nodes in the neck that show no evidence of cancer along with the thyroid, or removing only the thyroid. Eligibility: \- Adults age 18 and older with PTC or thyroid nodules suspicious for PTC, with no evidence that the disease has spread in the body. Design: * Participants will be screened with medical history, physical exam, blood tests, scans, and x-rays. * Participants will: * Answer questions. They may have a tumor biopsy. * Have a flexible laryngoscopy. A small tube will pass through the nose to the vocal cords. * Group 1: have surgery to remove the thyroid gland only. Lymph nodes in the neck will be removed if the cancer has spread. * Group 2: have surgery to remove the thyroid and lymph nodes in the neck. * At all post-surgery visits, participants will answer questions and have blood drawn. In addition: * 1 day: laryngoscopy. * 2 weeks: possible laryngoscopy. * 3 months: ultrasound of the thyroid and neck. * Discuss whether to try hormone treatment and/or radioactive iodine. * Possible diagnostic whole body radioiodine scan (WBS). Participants will swallow a capsule or liquid and lie under a camera. * 6 months: ultrasound and maybe laryngoscopy. * 1 year: diagnostic WBS and ultrasound. Participants may get thyroid stimulating hormone. * Participants will have annual follow-up visits for 10 years. They will have a physical exam, blood drawn, scans, and may complete a questionnaire.