A simple, lightweight transmission for use in an electrically powered vehicle is disclosed. The transmission is symmetric in both weight and power distribution, and provides two input-to-output gear ratios, a neutral setting, and a park setting. A single “dog” clutch operates in splined relationship with a first shaft, and a single planetary gear assembly is connected to a second shaft. Sliding the dog clutch among four positions serves to shift the transmission among direct shaft engagement for direct drive, engagement through the planetary gear assembly for overdrive, disengagement for neutral, and double engagement for park. Preferred embodiments include reduction gears in the planetary gear assembly. Other embodiments include a synchronizer so as to synchronize the shaft rotation speeds when they are not exactly matched. Further embodiments include a dual-servo shift mechanism that prevents shifting into park unless a park servo is in its park position.