According to my post-week 17 thread Click Here (The W), I have Cleveland picking 20th (given to Dallas), as the team with the best record that didn't make the playoffs.
According to the NFL Click Here (nfl.com), they have the 22nd pick (Dallas, actually).
It looks like now that it is regular season order regardless on playoff berth, except for the Super Bowl teams. I guess this is new for this year?
Old draft order, New draft order (20-29 only): 20 Dallas (from Cleveland 10-6), Tampa Bay 21 Tampa Bay 9-7, Washington 22 Washington 9-7, Dallas (from Cleveland) 23 Pittsburgh 10-6, Pittsburgh 24 Tennessee 10-6, Tennessee 25 Seattle 10-6, Seattle 26 Jacksonville 11-5, Jacksonville 27t San Francisco (from Indy 13-3), San Diego 27t Dallas 13-3, Dallas 29 San Diego 11-5, San Francisco (from Indy)