Thousands of patients suffer severe brain injuries every year, from causes such as trauma, stroke, and infection. Extensive clinical research in weaning from mechanical ventilation has led to recommendations for prompt extubation following a successful trial of spontaneous breathing in general intensive care unit (ICU). However, little evidence exists to guide decisions about when to remove the breathing tube in patients with severe brain injury. It is unclear which of the following strategies would optimize important patient outcomes: prompt extubation vs. prompt tracheostomy vs. waiting and extubating or performing a tracheostomy, timed according to physicians' discretion. Each strategy has associated risks: prompt extubation may lead to higher rates of extubation failure and reintubation, prompt tracheostomy may lead to an excess of unnecessary procedures, and waiting longer may expose patients to complications from prolonged mechanical ventilation.This trial in brain-injured patients will test will of the following will lead to better patient outcomes: (1) removing the temporary breathing tube promptly; (2) performing a tracheostomy promptly; or (3) the usual treatment you would have received if you were not enrolled in this trial.