Provided are orthodontic appliances and related methods in which at least one region of at least one sidewall of an archwire slot is tapered relative to an opposing sidewall. This feature can allow the archwire slot to conform to the slight twist that occurs in the archwire when the archwire is placed in asymmetric torque. Advantageously, this feature can distribute the contact stress between the archwire and appliance over a much larger surface area compared with conventional appliances, leading to a dramatic and surprising increase in torque strength and providing other ancillary benefits.