How can I get my caller ID to NOT show up when using a prepaid phone card?

This is sort of similar to/the opposite of the already-answered "How can I get my caller ID to show up when using a prepaid phone card?" question. (http://ca.answers.yahoo.com/question/index?qid=200... Only when I make a call to my local OneSuite #, OneSuite can tell what # I'm calling from even if I dial *67 first; ZipDial works, and the called party gets my phone # too! However, *67 does work as it should when I dial other #s, like my cellphone. I want to be able to make calls w/o giving out my # sometimes. I've looked at http://en.wikipedia.org/wiki/Caller_ID already.

I tried with an MCI prepaid card too; same problem. Strange.