You are thinking supplemental draft.
I am talking about a compensatory pick in the regular April draft. Cowboysrock said he didn't think we had ever been awarded a third before... I was sure we had. And we were - in 2001, and we spent the pick on Willie Blade. See here:
2001 NFL Draft - Wikipedia
Pick 93, the asterisk is for a compensatory selection.
That does seem to be the only time we'd ever received a third as a compensatory pick though. I wonder what free agent loss that was for? Would have been a 2000 offseason departure.
Edit: As I think about it -- relatively sure it was for the loss of Randall Godfrey to the Titans.