I need to transform some data from PSA56 to NAD83. It doesn't have to be that rigorous as it's purely for a context map. I'm guessing I will need to go to WGS84 and then to NAD83. If anyone has any suggestions for best practice please let me know. Using ArcGIS10
You are trying to impose a North American Datum on South America data which does not work.
PSAD stands for Provisional South American Datum developed in 1956.
I would highly recommend you convert it to WGS 84 and assign the UTM zone if you have to do it for a particular country, region etc. This should resolve your issue.
If you do not know which UTM Zone you have to apply refer to this link which could be helpful.