The team's owner and general manager spoke with confidence on Friday after selecting perhaps the draft's finest quarterback chaser with the No. 60 overall pick.
"I think it gives us enough confidence that we can work through some of the issues that have basically caused him to drop and maybe improve on that," Jones said. "That's certainly the plan and have us a heck of a contribution to winning."
Gregory tested positive for marijuana at the combine, and was late to pre-draft interviews, according to NFL Media Insider Ian Rapoport. Worries also exist about the defender's ability to handle the "mental rigors" of the NFL, per Rapoport and NFL Media's Albert Breer.
"In Randy's case, obviously there are some off-the-field concerns that we had," coach Jason Garrett said Friday. "That's one of the reasons a player so high on our board slid to the bottom of the second round. We had him in here and spent a lot of time with him.
" ... But as Mr. Jones alluded to, we feel like that's the responsibility of our support staff as well. We take great pride in that, we've had other players who have had different off-the-field issues that we feel like we've helped them with. So in terms of those off-the-field issues that Randy has, we feel that we can help him address those."
Gregory's slide was the product of 31 other teams unwilling to take on the baggage he brings into the pros. If Dallas can make this work, they've addressed a roster need with one of the better pass rushers to come along in some time.