Whether Daryl Morey was endeavoring to change the subject or give himself a high bar to clear, he did not lower expectations heading into free agency.

The Rockets are well over the salary cap, leaving them only the mid-level exception of roughly $5.7 million to offer. But Morey said the goal is to one way or another come away with a third star. Failing that, he said, he hoped to spend the mid-level money on a significant addition that would likely be coming down to the Rockets' price.

Sharing the hope to land a third star could have been a way to spread the word that the Rockets still consider Chris Paul to be a second star. Morey strongly denied that Paul asked to be traded and similarly refuted a notion that the Rockets were looking to clear his enlarged salary from the books.

The Rockets, however, plan to begin free-agent shopping trying to pull off a coup similar to landing Paul two years earlier, this time with an expected pursuit of 76ers forward Jimmy Butler and in free agency, rather than in an opt-in trade as Paul engineered.

Butler could opt in to the final season of his contract, worth $19.84 million, to facilitate a trade to a team he would choose as a free agent. But the expectation is that Butler will become a free agent and attract a much larger contract.

The Sixers will be determined to keep him and will have Bird rights to offer the kind of contract that would be difficult for the Rockets to match. But Butler, like Paul in 2017, could want to play with James Harden. He and Harden are extremely close, and Butler is expected to at least consider the franchise the Tomball native considers his hometown team.

Failing at the third-star plan, Morey has said he would want to use his mid-level exception to land a starting-caliber player, rather to spread it around to multiple players to fill out his diminished bench.

With that in mind, he would have to go into a free agency with a much larger pool of options, hoping that someone that would likely expect more than mid-level will sign for what the Rockets have to offer.

Some of the developments leading to July could help with that, with so much of free agency about reacting to the chain reaction.

Harrison Barnes opting out of a contract to have been worth $25.1 million next season would not seem to impact the Rockets, unless he was giving up $25.1 million in the hopes of earning $5.7 million. But every free agent that joins the class of 2019 at a higher price, with Khris Middleton as expected also joining the crowd of expensive free agent wings, increases the chance that someone expecting more opts to play for the mid-level exception the Rockets and other contenders have to offer.

There is a long list of players that could fit that scenario, even if most will likely be priced out of the Rockets' mid-level range.

A look at some of the players in the pool of potential Rockets' mid-level targets:

Reggie Bullock, Lakers forward

Bullock is very much the sort that could be priced out of the Rockets' range, but is likely to be on the move and has skills as a catch-and-shoot threat that would fit well with the Rockets. He is a career 39.2 percent 3-point shooter with switch ability on the defensive end.

DeMarre Carroll, Nets, forward

Briefly a member of the Rockets, Carroll would bring the toughness on the wing that would appeal to the Rockets and would offer another small-ball option at power forward. He can knock down 3s, but is not a particularly high percentage range shooter.

Wesley Matthews, Pacers, guard

Matthews is a tough defensive player and a good shooter that the Rockets hoped to land during the in-season free agent market. He chose the Pacers to get more playing time than likely with the Rockets to set himself up better for free agency. That would indicate he is unlikely to come at a bargain price.

Wayne Ellington, Pistons, guard

Shooting is getting expensive and Ellington has made 37.9 percent of his 3s in his career while putting them up at a Rockets-like rate (at least 6.2 per game, usually off the bench) in the past five seasons. After 10 NBA seasons, he could be especially hesitant to choose a contender at a discount compared to richer offers.

Kentavious Caldwell-Pope, Lakers, guard

The Rockets had interest in Caldwell-Pope early in the season and could find him available during the Lakers' house-cleaning. He has averaged in double figures in each of the past five seasons since his rookie year with the Pistons. He made 34.7 percent of his 3s last season after a career-best 38.3 percent the prior season, his first in Los Angeles.

Rondae Hollis-Jefferson, Nets, forward

The Nets opened cap space by declining to make Hollis-Jefferson a qualifying offer. Hollis-Jefferson is a versatile defender and a reliable scorer, but has been nowhere near the sort of 3-point shooter the Rockets typically seek, making a career-worst 18.4 percent of his 3s last season.

Tomas Satoransky, Wizards, guard

A fine shooter, Satoransky has good size and athleticism, as he demonstrated with a memorable dunk all over Zhou Qi. He has made 40 percent of his 3s in three NBA seasons.

Kelly Oubre, Suns, forward

Oubre has many of the qualities the Rockets could seek and might be interested in a homecoming. He appears to be a player that should be a more reliable range shooter, but he remains at 32.1 percent for his career.

Darius Miller, Pelicans, forward

Miller is not as accomplished in a more limited role as many others hitting the free agent market, but he is a career 38.2 percent 3-point shooter.

Rodney Hood, Trail Blazers, forward

Hood likely helped his stock with his strong playoff performances, leaving the Jazz and Cavaliers years behind. That also would likely elevate him put of mid-level range, but he could be a guy that leaves someone else standing when the larger money is gone.

JaMychal Green, Clippers, forward

Though not a wing, the Rockets could use another 3-and-D at the four, too. Green made 40.3 percent of his 3s last season with the Grizzlies and Clippers, likely making him an expensive free agent.

Trevor Ariza, Wizards, forward

Run it back? It would seem unlikely that Ariza would sign for the mid-level exception, even more so that he would return to the Rockets for a third tour of duty in Houston. But since the Rockets are still trying to replace Trevor Ariza, he would seem to fit the mold.