AirPlay mirroring poor performance

Mirroring from my iPad mini 2nd gen (or retina MBP 15in 2015) to new Apple TV 4th gen barely works. Trying to stream a movie from the iPad stalls so badly that the movie is unwatchable. I turned off all other devices on the wifi network, but no improvement. This is the primary reason I bought the Apple TV, so unless I can get mirroring to work, it's going back to the store. I restarted the devices, updated software, but no change.