Dolphins general manager Jeff Ireland spoke this offseason of his desire to add more pass-rushers to complement Cameron Wake, adding that “you can never have enough.”

As it turns out, the Dolphins’ only skilled pass-rushing additions who made the team were rookies: Olivier Vernon, who had six sacks two years ago at the University of Miami but just 1 1/2 in six games last season, undrafted defensive end Derrick Shelby (11 sacks in four years at Utah) and developmental linebacker Sammy Brown, claimed off waivers last weekend.

If the Dolphins do not generate consistent pass rush beyond Wake — beginning Sunday at Houston — an already thin secondary will be further exposed against sophisticated passing games.

With Wake likely to attract frequent double teams, “the guy with the one-on-one blocking needs to win,” defensive tackle Randy Starks said.

Last season, the Dolphins produced 41 sacks and finished 13th in the league in sacks per pass play. But the players who produced 12 of those sacks are gone, including Jason Taylor (seven).

Making up for loss

Conversely, the Dolphins added players who generated just 2 1/2 sacks in the NFL last season — both defensive backs: Richard Marshall and Troy Nolan.

So who will make up for the loss of Taylor and those 11 sacks?

Start with defensive ends Jared Odrick and Vernon.

“Odrick has had a good camp,” coach Joe Philbin said. “We see some development on tape. Now it’s time to see that production against somebody else. He’s prepared himself well.”

Odrick, a full-time starter for the first time, produced five sacks and 16 quarterback hurries in 597 snaps last season.

Expected to shift from defensive end to tackle on third downs, Odrick believes double figures in sacks is realistic.

“This is a big, big year for him,” Taylor, now an ESPN analyst, said at his charity event this week. “I expect he’ll be fine. I thought he had a great year last year, really growing.”

Miami had six sacks in four preseason games, none by Odrick. Wake had 1 1/2, Vernon, Shelby and rookie Kheeston Randall one apiece. Two players no longer on the team also had sacks: Isaako Aaitui (1) and Jamaal Westerman (1/2).

Vernon, who likely will play on third-and-longs and other obvious passing situations, said he hasn’t generated as much pressure on the quarterback as he wanted in preseason but believes he improved the last two games.

Tougher league

“The biggest difference from college is the offensive linemen here don’t make mistakes,” Vernon said. “They know our tendencies. It’s not easy to get a sack in this league. Sometimes, when I’m trying to bull-rush the tackle, they’ll pull your pads down and make you fall forward. That never happened in college. I have to get used to that.”

Wake said Vernon has “got the right temperament” and has “that pit-bull mentality as an undersized end.”

The Dolphins hope Wake’s sack totals are closer to his 14 from 2010 than the 8 1/2 in 2011. In Wake’s defense, he had more quarterback pressures that any player in the league last year (52) and also drew the most holding penalties from offensive linemen (13), according to Pro Football Focus.

“Football people know I had a better year last year than the year before,” said Wake, who is moving from outside linebacker to defensive end in Miami’s new 4-3 base. “Out of the 13 holding calls, what if six had been sacks? Then the [sack] numbers would have been the same.”

Starks’ sacks dropped from 7.0 in 2009 to 3.0 and 4 1/2 the past two years. He expects to generate more pass rush as a defensive tackle in the 4-3 defense.

“It’s easier as a pass rusher in a 4-3 because I’m more of an inside rusher,” Starks said. “In a 3-4, I do a lot of that from the outside, and I’m not exactly a speed guy like Wake.”

No help here

The other starting defensive tackle, Paul Soliai, has two sacks in five seasons (both in 2010) and likely will not play much in obvious passing situations.

The Dolphins’ linebackers will get some pass-rushing opportunities — mixed with coverage responsibilities — but they say that will vary.

Karlos Dansby, who is moving to middle linebacker in a 4-3, once had eight sacks in a season for Arizona (2006) but two for Miami last year. Kevin Burnett’s sacks dropped from six in San Diego in 2010 to 2.5 here last year.

And Koa Misi, who had 4 1/2 sacks as a rookie in 2010, had just one last season but expects to have “a little” more pass-rushing opportunity in his new SAM linebacker role.