Aspects of the technology relate to exception handling for a vehicle. For instance, a current trajectory for the vehicle and sensor data corresponding to one or more objects may be received. Based on the received sensor data, projected trajectories of the one or more objects may be determined. Potential collisions with the one or more objects may be determined based on the projected trajectories and the current trajectory. One of the potential collisions that is earliest in time may be identified. Based on the one of the potential collisions, a safety-time-horizon (STH) may be identified. When a runtime exception occurs, before performing a precautionary maneuver to avoid a collision, waiting no longer than the STH for the runtime exception to resolve.