In Canada, shift trades (we call them MUTEX - mutual exchanges) are very common. Most times, they are used to extend vacation leave or to take a day off when there are no leave places available.
Additionally, we have the ability to do a self-MUTEX. In this case, the controller can do a shift trade with himself. HE can move a day of work to a day of rest, provided the day he trades to is worked in advance. THe self-MUTEX is at management discretion, but is rarely denied. Regular shift trades between controllers is never denied unless in unusual circumstances.
The ability to do this is written in our contract.