Dial() 'h' and 'H' not working (hang up by pressing *)

I’ve got two basic SIP phones running though Asterisk. They have no issue dialing extensions, but if I initiate a Dial() call with the flags for detection of * being dialed, the Asterisk box never sees the * when it’s pressed.

Maybe I need another flag set in order to make sure Asterisk monitors the audio for the * sound (or however these SIP phones send that data).