Aspects of the disclosure provide a of generating and following planned trajectories for an autonomous vehicle. For instance, a baseline for a planned trajectory that the autonomous vehicle can use to follow a route to a destination may be determined. A stopping point corresponding to a traffic control that will cause the autonomous vehicle to come to a stop using the baseline may be determined. Sensor data identifying objects and their locations may be received. A plurality of constraints may be generated based on the sensor data. A planned trajectory may be generated using the baseline, the stopping point, and the plurality of constraints, wherein constraints beyond the stopping point are ignored.