A Witness Elite what? The Elite series is their match/target gun line. There a a number of guns with Elite in the name, none of which would be considered carry guns.
I have a Witness Elite Match in .45. Nice gun. Way better quality than the price would suggest (no pot metal in sight). That said, it would NOT be my first choice for concealed carry.
If your serious about carrying a Witness, I would suggest you look at the the Witness Steel Compact or the Witness Polymer Compact or Carry models.