Sandra,
Areas that I have worked on to make 'Off-Shoring' successful were to ensure a strong Governance structure was in place with financial implications for missed, agreed upon, SLA requirements. I personally would focus on tracking of what is being received (sample testing on your side as well to ensure quality) and ensuring the supplier of your Off shore services knows you are tracking (but not necessarily what)and keeps providing you regular status reports. I have seen significant $ wasted when you don't keep track of what has been asked for or if you don't put penalties in place for missed SLA's...hope this helps