Does Outsourcing really work?

At this moment my company has outsourced some processes (hire, termination and organizational change) for a number of pilot countries to an off-shore service provider.
The data entered by the service provider is limited and standard documents - that have to be filled out by local HR - have been implemented. Furthermore, a step by step diagram of each process has been drawn and provided to the service provider.
The training and follow up of the service provider is in the hands of one local person. The results after a few operational months are positive.
This shows that outsourcing a well defined, well structured, strictly limited task can work !