If history indicates what they'll do, it points to drafting a cornerback. Houston has never taken a running back in the first round and a number of Texans officials employ the Denver mindset that a lower-round running back can be just as effective as a high pick in their system.
The departure of Robinson, the 10th overall pick in 2004, leaves Houston without its most consistent player in the secondary over the past several years. The Texans have always had trouble dealing with Peyton Manning and AFC South foe Indianapolis, and the loss of Robinson could make things worse.
They have veteran Jacques Reeves and up-and-coming second year player Glover Quin, along with fourth-year pro Fred Bennett. But it's unclear if any of those players can step up to fill in for Robinson.
Houston tried to beef up the unit before the draft, courting free agent cornerback Leigh Bodden before he opted to stay with New England.
Texans general manager Rick Smith knows cornerback is a need, but didn't indicate if it's his biggest priority.
"I think it's important," he said. "Any time you lose a player like Dunta, who plays at the level that he plays, you've got to think about how you replace that. I do think we've got some young players on our football team that perform well ... so we're not depleted at the position, but you still are looking for impact players whenever you lose a player of his caliber."
If they decide to use the pick on a cornerback, Boise State's Kyle Wilson could be a good choice.
However, this might be the year the Texans nab a running back in the first round after lacking a solid running game for years -- with the exception of Slaton's excellent rookie season of 2008. The smallish Slaton, taken in the third round by the Texans, had a breakout rookie season, rushing for a franchise record 1,282 yards and giving the team hope the running problems were over.
Instead he fell into a sophomore slump, fumbling seven times and rushing for just 437 yards before a nerve problem ended his year in early December. The surgery to correct that condition was successful and he should be healthy in time for the season. Even if he is, last year showed that the Texans need a bigger player to complement the 5-foot-9 Slaton.
An attractive option with this pick could be Fresno State's Ryan Mathews. The 6-foot Mathews ran for 1,808 yards and 19 touchdowns in 2009 and amassed 3,280 yards and 39 touchdowns in three college seasons.
NFL draft consultant Gil Brandt has been impressed with Houston's recent success in the draft. He pointed to middle linebacker DeMeco Ryans, the first pick in the second round in 2006, and to Quin, taken in last year's fourth round.
He can see the Texans choosing a running back first this year.
"I think if I were there (at 20) and I wanted a running back, I think I might just try to move down a few spots and know that I had a chance to get a pretty good running back at 25 or 26," he said. "That's probably who I would take, because I'm not sure -- I just don't know on the West Virginia running back (Slaton) how he can hold up because he is not really a big guy, whereas if you get somebody like Ryan Mathews, I know they're going to hold up pretty well."
Smith believes talented running backs can be found beyond the top two rounds.
"I know we had some success in Denver with later rounds, picking backs that were productive," he said. "So I think what you have to do as an organization, in my opinion, is you've got to have some real clarity with ... what you look for in all positions across the board, and to the degree that you can identify those traits and characteristics and then go find those characteristics, I think you can find value all the way through the draft and in free agency."