As ESPN.com’s Marc Stein reminded us this week, the league is running out of players eligible for the amnesty provision — that sexy and often misunderstood minx in the new collective bargaining agreement that allows teams to guillotine one player from their cap sheet. Teams were/are allowed only one bite at the amnesty apple over the length of this CBA. Use it on Charlie Bell’s expiring $4.1 million deal and you’re scrambling to offload $20 million in dead money to gain cap flexibility for Andre Iguodala or Dwight Howard. Pull the amnesty trigger on Chauncey Billups to slip Tyson Chandler into space, and you’re stuck with Amar’e Stoudemire, forever and ever, amen.

Teams can use the amnesty only on players working under contracts signed before the lockout, and only when said players are still on the same team they were on when the lockout started; players traded since then are not eligible for that sweet, sweet amnesty relief. Teams must still pay the players their amnesty.

Under these rules, a few teams — Memphis, San Antonio, Boston, Utah — have no realistic amnesty candidates, which is why it might have been sort of cool had the new CBA allowed such teams to trade their amnesty rights as they can any other asset. (Note: I realize this would have brought complications, especially in allowing trade partners two potential amnesty chances, but it’s fun to think about.) Below is a team-by-team look at the few realistic potential amnesty cases still on the books as the league reopens for official business. Some of the figures are approximate, especially the estimated savings, since we only estimate how teams would replace amnestied players, and how much under-the-cap teams might bid on amnesty victims. (Those teams pick up a portion of the player’s salary from that player’s old team.)

Chicago Bulls: Carlos Boozer

This might be the trickiest case of all. The most likely scenario has long been that the Bulls wait until next summer to finally amnesty Boozer, since doing so now would not open up any salary cap space. The Bulls also consider themselves a title contender if whole, and the lag time between the start of free agency and the league’s amnesty window means that Chicago would have no ready means to replace Boozer’s production on offense.

It’s easy to overlook what Boozer brings on that end. He’s a minus defender, and Tom Thibodeau has often left him on the bench in favor of Taj Gibson during fourth quarters of close games. He’s slow, flat-footed, and he yells a lot. And for all his alleged offensive skills — some of which are clearly in decline — the Bulls scored more efficiently with Boozer on the bench last season, and at nearly identical rates in 2011-12 regardless of whether Boozer was on the floor, per NBA.com. The Bulls blew the league away on both ends with the Taj Gibson–Joakim Noah pairing in 2011-12, and in many more minutes last season Chicago scored above its overall rate with those two on the floor, per NBA.com — even without Derrick Rose, and with Jimmy Butler only just discovering what he can do on offense. Could the Bulls be ready to move on from Boozer?

Maybe. But there is risk in this defense-first team surrendering a well-rounded offensive big man, especially with Rose recovering from knee surgery. The Bulls struggle for spacing, and they’ve made up for that by building many of their pet sets around the ability of both Noah and Boozer to do lots of things from the high post area. Boozer can shoot from there, providing some valuable air space, and he’s one of the best passing big men in the league. His post-up and off-the-bounce game are falling off with age, but Boozer is smart and keeps the ball moving in a way that works for Chicago.

Even if the Bulls want more of the Gibson-Noah duo, they can still use Boozer to prop up reserve-heavy units. And they’d feel the trickle-down effect without Boozer. Dumping him would leave Chicago with only three rotation big men, meaning they’d rely upon Nazr Mohammed or some bottom-of-the-barrel free agent for important minutes — even if they extend last year’s use of small-ball lineups, partly an emergency response to injuries, into next season.

Luol Deng’s contract is expiring, and with Butler rising into something like a proto-Deng, the easiest way to cap flexibility next summer is to let Deng walk and save the Boozer amnesty bullet for that time.

But the cost of this team, as things stand now, is going to be enormous as the league’s new tax rates kick in. The Bulls payroll is going to move at least into the $81-$82 million range as they fill the roster, meaning Chicago will come in about $10 million over the new tax threshold. Factor in the harsh new penalties, and the Bulls are set to pay something like $96 million to field this roster. Keep in mind: Jerry Reinsdorf, the Bulls’ owner, has paid the luxury tax exactly once in 10 years — last season, when the Bulls plopped a $3.9 million tax bill atop their $74.3 million payroll, for a total payout of about $78.2 million.

Is Chicago really ready to pay $18 million more than that this season, when slicing away Boozer could save them something like $12 million, factoring in replacement costs?

Chicago could find other ways of saving some scratch — salary-dumping Kirk Hinrich during the season, or even dealing Deng’s expiring contract if they feel comfortable doing so. Huge salary dumps might be a little harder during the season than they used to be, since teams are rushing to reach the league’s new (and higher) salary floor now instead of hoarding space into January and February. But there are always other avenues for savings.

The most likely scenario remains for the Bulls to keep Boozer one more year. But the cost, plus the potential for Rose to carry more Gibson-Butler minutes, makes an accelerated Boozer-ectomy at least worth considering.

Miami Heat: Mike Miller, Joel Anthony

After re-signing Chris Andersen to a deal that will pay him about $1.7 million next season, the champs are set to shell out about $87.3 million to 13 players — not including James Ennis and Jarvis Varnado. That would place them about $15.6 million over the new tax line, and that little .6 there is significant. That $600,000 creeps into the fourth incremental tax bracket, and the Heat would have to pay $1.95 million in taxes just for that little $600,000 in salary. The total bill for this roster would be an astronomical $117.9 million, not quite what the Lakers paid overall last season, but enough to make a mid-market team blanch. (And as Brian Windhorst points out, it might even be a tick higher, depending on some small variables.)

Some savings are in order. Mike Miller has long been the most obvious candidate, since he’ll make a hefty $6.2 million next season and barely plays amid an endless stream of injuries. But Miami’s LeBron-centric small-ball attack requires 3-point shooting, and Miller, despite his limitations as a defender, seems to become important again every June. Slicing away Miller’s salary would net a whopping $15 million in savings, though the Heat would have to spend at least $1 million or so on a replacement. Is $15 million worth losing Miller, with both Shane Battier and Ray Allen aging?

The safer alternative, in on-court terms, is cutting Joel Anthony, a beloved but basically useless piece at this point. He makes only $3.8 million, and his salary is flat (Miller gets a $400,000 raise in 2014-15), but cutting him would save Miami about $9.5 million before replacement costs. Cutting Miller brings about $5.5 million more in savings, but carries more basketball risk. What would you do?

Los Angeles Lakers: Metta World Peace, Kobe Bryant, Steve Blake

The tax crisis isn’t quite as urgent without Dwight Howard’s $20 million salary slot, but the Lakers are still going to finish with a payroll in the $83.5 million–plus range once you factor in Chris Kaman, Jordan Farmar, and various minimum-salaried pieces to flesh out the roster. That would leave the Lake Show about $12 million over the tax line, for a Total Payroll Suffering Bill of about $104 million. That’s a pretty expensive no. 8 seed (or trip to the lottery), especially when tanking is staring you in the face as a cost-effective option that would be much more helpful in the long haul.

World Peace is by far the most likely casualty here, and the two sides are still talking about the possibility now. Ditching him would save the Lakers nearly $15 million, twice World Peace’s salary, before factoring in some cheap replacements. Lopping off Bryant’s massive $30.5 million has long been the sexier talking point, but without Howard on the books, going this route saves the Lakers only about $4 million more than the World Peace path. That $4 million figure undersells the gap a bit, since teams would surely bid more on Kobe than on World Peace, but the giant distance between their salaries means the Lakers don’t stand to gain quite as much in pure financial terms as they once did via amnestying Mamba.

One added bonus of cutting Kobe: It would take the Lakers under the tax line after two straight seasons as taxpayers under the new CBA. Any team paying the tax four times in five seasons is subject in that fourth season to a crazy super-tax, so stopping the clock at two seasons has value. The Lakers might be safe from the tax goons in 2014-15 with just Steve Nash on the books, but you know this team is going to reload eventually.

Using the amnesty provision on Pau Gasol might get the Lakers a shade under the tax, depending on how they fill the rest of the roster, but Gasol might be movable in a trade. Blake is another option, but he makes just half of World Peace’s salary and thus brings less in savings. If you’re going to be mediocre or bad either way, might as well take the cheaper way.

Milwaukee Bucks: Drew Gooden

For the record, I’m rooting against this because I enjoy ridiculous things. The amnesty provision is made for players like Gooden, but the Bucks have simply refused to amnesty him, and at this point, they should just take the inanity as far as it will go — if it remains possible to do so after the Bucks agreed late Wednesday to take Luke Ridnour into cap space and tendered a four-year, $32 million offer sheet to Jeff Teague. This is like sitting through the last 45 minutes of Gone With the Wind even though you hate it, or when Kramer and the car dealership guy decided to see how far the test drive car would go after the gas gauge hit “E.”

Gooden has appeared in 107 games combined over the first three years of a contract that somehow has two seasons remaining and pays him nearly $7 million per season. The Bucks have approximately 27 big men already under contract. Gooden logged 151 minutes last season and was more valuable as a Twitter comedian than as a basketball player. The only reason he is still on the Bucks is that ownership (understandably) finds the idea of paying a guy to play somewhere else a tad distasteful.

But the Bucks have some glaring holes still on the roster and a finite amount of cap space with which to fill them. They need to finish up their best-of-seven “shoot” with Atlanta for first choice between Teague and Brandon Jennings (pick odds, Milwaukee!), and it’s probably a good idea to find at least one veteran wing player beyond O.J. Mayo and Carlos Delfino. Count all of Milwaukee’s agreed-upon trades and signings before the Teague offer sheet, including Jennings’s $8 million cap hold, and you arrive at a total salary bill of about $54.2 million — not including Giannis Antetokounmpo, who will likely stay abroad this season, Nate Wolters, or any money for the last three roster spots. (This scenario assumes the Bucks renounce the giant cap hold attached to Monta Ellis, who apparently does not have it all.)

That would leave only about $4 million for Teague’s $8 million offer sheet, which obviously doesn’t compute. Waiving Gustavo Ayon’s $1.5 million non-guaranteed deal doesn’t get the job done, either. This would seem to necessitate the Bucks either renouncing their rights to Jennings or pulling the plug on our lovable protagonist. It’s possible for Milwaukee to delay one of its big signings in order to resolve the Jennings-Teague non-fight first (and perhaps even sign-and-trade Ellis), but as long as the Bucks are operating under the cap, one large chunk of salary has to go in order to make this whole thing work. Fingers crossed it’s not Gooden, people. Fingers crossed.

Sacramento Kings: John Salmons

The final veteran residue of one of the most depressing trades in recent league history — the Kings-Bucks-Bobcats three-team shrug on draft day 2011 that sent Stephen Jackson, Corey Maggette, Beno Udrih, and Salmons flying around the league until each of their new teams, respectively, decided they didn’t want the players they received anymore.

The Kings were the undisputed losers in that deal, having acquired the player with the longest contract (Salmons) in order to move three spots down in the draft and select Jimmer Fredette. Seriously, this was a masterpiece of terrible trading by the Kings. This is Geoff Petrie’s Guernica.

The Kings are right at the edge of the cap after dealing a second-round pick (and swap rights on another) to Milwaukee for Mbah a Moute and splurging on a four-year deal for the very solid Carl Landry. They could have kept Tyreke Evans, much younger than either of those players, for about the same money they will pay them combined, or they could have paid none of the three and gone into tank mode. That’s a dicey move for a new ownership group seeking to fill its current arena while negotiating for a new one and re-earning the loyalty of a fan base that has seen far too much losing. Mbah a Moute will bring defense and maturity to a roster in desperate need of both, and Landry will compete for minutes in a crowded big-man rotation while turning each member of that rotation (save DeMarcus Cousins) into a trade chip. The Kings still won’t be very good, and on balance I’d rather have the second-round pick, more in-season cap flexibility, and a shot at Andrew Wiggins. But the Kings are working under a lot of competing pressures.

They’ll need more than what they have now to be remotely competitive in the Western Conference, and more than what piddling room the exception can get them. Amnestying Salmons opens up a midlevel salary slot.

Toronto Raptors: Linas Kleiza

Kleiza has always been a more likely Raptor amnesty cut than Andrea Bargnani, but with Bargs in New York (and wearing Ray Bourque’s number), Kleiza becomes the only candidate on the board. The Raptors don’t really need him. Kleiza has barely played in three seasons in the T-Dot, and there won’t be a lot of minutes for him with Tyler Hansbrough onboard and Dwane Casey curious about how Rudy Gay might function as a small-ball power forward. The Raptors project at about $1.75 million over the tax, meaning using amnesty on Kleiza’s $4.6 million would take them under it — wiping out a $2.6 million tax bill and giving Toronto access to the revenue-sharing distribution for teams that come in under the tax (about $1.47 million per team last season). That’s not nothing.

But the Raptors might also be able to net a second-round pick in exchange for Kleiza’s expiring deal at the trade deadline if he shows glimpses of his old game. Is banking on that possibility better than about $4.3 million in certain total savings? They could also deal Kleiza for a player they actually like (but some other team doesn’t) and duck the tax by coming to a cheap buyout agreement with Marcus Camby.

Detroit Pistons: Charlie Villanueva

The Pistons have no such tax pressures, and may value Villanueva’s very limited trade value (second-round pick, max) as an expiring contract more than the cap space they could open up by saying good-bye. Detroit is right at the cap line after agreeing to terms on a small two-year deal with old pal Chauncey Billups (as reported first by Yahoo!’s Adrian Wojnarowski). Detroit has about $55.5 million in committed salary now, though the precise figure depends on what they want to do with a few non-guaranteed players — Kim English, and second-round picks Tony Mitchell and Peyton Siva. Regardless, they’ve got no meaningful cap space left, and dumping Villanueva’s $8.6 million salary is the only way to change that. Expunging him would also open up some roster flexibility, since Detroit now has 14 players guaranteed money next season — one short of the limit — before accounting for English, Siva, and Mitchell.

But the financial need here isn’t urgent, and Villanueva showed flashes of value last season (finally!) as a floor-spacing power forward on bench units centered around Drummond pick-and-rolls. Those lineups struggled on defense, but the three that logged at least 30 minutes together scored at ridiculously high rates, per NBA.com. Still: The Pistons will have more shooting next season with Luigi Datome and Kentavious Caldwell-Pope, and Villanueva provides zero defense or rebounding despite his size.

The signings of Billups, Will Bynum, and Italian League MVP Luigi Datome also address the need for a backup ball handler and wing shooting. It would not surprise me if Billups opened the season as a starter, since slotting the Brandon Knight–Rodney Stuckey pairing around the Josh Smith–Drummond–Greg Monroe frontcourt amounts to spacing death.

Detroit also keeps the so-called room exception, worth about $2.65 million, in its pocket if it wishes to sign another low-value veteran free agent down the line. The odds are much better than 50/50 that Detroit keeps Villanueva around, but that could change. Enjoy Amnesty Fever while it lasts.