In the hierarchy of baseball trade satisfaction, nothing beats a blockbuster: The more teams and talent, the merrier. We’ve already seen one such swap this month, and unless the latest David Price sweepstakes turns into another tease, we’re in for another in the next 10 days. Most moves don’t merit as much attention as the rare deal involving an ace or top-tier prospect, but the second-most satisfying type of trade — an efficient exchange of lower-profile, complementary pieces in which each team draws from another squad’s surplus to land precisely the player it’s been missing — imparts almost the same sense of fulfillment by bringing greater balance to the baseball world.

In its pleasing symmetry, this type of transaction is the baseball equivalent of one of the Internet’s most soothing sites: Things Fitting Perfectly Into Other Things. TFPIOT, which hit Tumblr in 2013, houses a user-submitted collection of photos and GIFs of unrelated objects that happen to fit together as tightly as a tennis ball and a chain-link fence (or, as it turns out, a tennis ball and at least one person’s drainage pipe). Its archive of items that appear to be (but aren’t!) made for each other serves as a tribute to serendipitous design and a comforting reminder that given enough permutations, even randomness results in order. The site’s front page, quoting a Digg description, promises to deliver a “certain kind of peace in an otherwise chaotic world,” and on most days, it does. There’s something about a package fitting perfectly into a mailbox that does more to restore one’s faith in happy endings than the last scene of When Harry Met Sally….

The lead-up to the July 31 non-waiver trading deadline is as chaotic as baseball’s slow-developing season gets (with the exception of the occasional photo finish). It’s the one period before September that consistently turns contenders into rebuilders, and longtime fan favorites into future opponents. This season’s unprecedented parity might limit trade activity; on the other hand, it might also ensure that each move matters more than usual. As exciting as it is to follow the annual game of midseason musical roster spots, the upheaval calls for the calming effect of a baseball edition of TFPIOT. We’ll call it Players Fitting Perfectly Into Other Teams.

Earlier this year, Diamondbacks third baseman Eric Chavez looked like the archetype of a potential perfect fit, a player who could slide so smoothly onto another roster that he’d seem to have been there since Opening Day. Since his troublesome back rose from its deathbed in 2012, Chavez has approximated the production of his early-aughts prime, albeit in a much more limited role. Although the veteran rarely sees a southpaw, his still-potent bat against opposite-handed pitchers would have made him appealing to a team like the Angels, who lack a lefty off the bench and whose defensively challenged, right-handed-hitting third baseman, David Freese, has struggled against same-sided pitching. The Braves and Tigers, who are playing Chris Johnson and Nick Castellanos at third, respectively, might have been equally intrigued.

Sadly, a knee strain sent Chavez back to the Azkaban-like confines of the 60-day DL, forcing him to consider retirement for the umpteenth time. However, a handful of healthy players who might be on the move have the potential to provide the same sort of seamless fit. Read about them below, then close your eyes and imagine them sinking slowly into a reassuring roster-spot receptacle: ahh, deadline anxiety dissipated.

Click here for more 2014 MLB trade deadline coverage.

Perfect Fit: 1B Adam Dunn and the Milwaukee Brewers

Closest Inanimate Object Equivalent: Baseball bat + tripod

Why He Fits: Dunn in the non-DH league? OK, it sounds like a stretch, but bear with me. Brewers GM Doug Melvin has many virtues, but finding first basemen hasn’t been one of them since Prince Fielder departed in 2012 and Corey Hart succumbed to the knee surgery that cost him all of 2013. Over the past two seasons, most of the Brewers’ stopgaps at the game’s premium offensive position have been miscast corner infielders (Alex Gonzalez, Yuniesky Betancourt — who’s back on the market!) and/or low on-base guys whose bats have seen better days (Lyle Overbay, Mark Reynolds). According to Baseball Prospectus’s Visual Depth Charts, only the DL-devastated Rangers project to get less from first base over the rest of the season than the replacement-level performance PECOTA foresees from the Brewers’ current Reynolds/Overbay righty/lefty time-share. Milwaukee’s offense ranks last among major league teams in percentage of non-pitcher plate appearances with the platoon advantage (40.0), but the position where the team has platooned regularly has been one of its weakest.

Enter Dunn, an impending free agent with whom the White Sox would be willing to part. The slugger would give the Brewers a big offensive boost relative to Overbay and a power threat from the left side of the plate, which their righty-heavy lineup has lacked all year. He’d also add some much-needed patience to a team that’s posted a lower walk rate than the offensively feeble Padres. Dunn, who’s still in search of his first playoff appearance, would get a chance to break his losing streak in a park that favors left-handed home run power to an even greater degree than The Cell, where the outfield walls are against him. And the rest of us would have at least two months to savor the spectacle of a Dunn/Reynolds duo, a platoon of two of history’s most Three True Outcomes–heavy hitters in the same city where TTO pioneer Rob Deer made his mark. Once you’ve pictured that pairing, baseball without it seems barely worth watching.

The only obstacle is Dunn’s defense, which has never been his strong suit. The Big Donkey started 70 games at first last season and posted dismal defensive ratings, but Jose Abreu’s arrival has held Dunn to 20 starts at first this year. Giving the 34-year-old a glove in the majority of Milwaukee’s games would be malpractice in most circumstances, but the offensive upgrade over the status quo makes the move worthwhile. Reynolds, who’s become a serviceable fielder at first, could minimize Milwaukee’s exposure by pinch hitting against lefty relievers late in games and replacing Dunn on defense.

Perfect Fit: C Carlos Ruiz and the Baltimore Orioles

Closest Inanimate Object Equivalent: Toy baseball + slinky + mug

Why He Fits: Orioles backstops other than Matt Wieters have hit .210/.265/.331 this season, making catcher an offensive abyss for Baltimore since mid-May. Acquiring Nick Hundley hasn’t helped, and while 28-year-old rookie Caleb Joseph leads the league in caught-stealing percentage and has proven to be a fine framer, his bat makes him more of an understudy than a leading man. The O’s, who hold the second-worst record of any first-place team, need help to maintain their modest lead in an uncharacteristically soft AL East, and with Wieters out for the year, catcher is the position at which they can make the most significant strides. Unfortunately, it’s also the position with the least meat on the market. Aside from Kurt Suzuki, a flawed receiver who’s ridden a BABIP boost to an unsustainable offensive start, there’s only one obvious answer: the Phillies’ Ruiz.

Ruiz remains a dangerous hitter and the best blocker in baseball, and while he’s signed through the next two seasons with an option for 2017, making a medium-term commitment might be in Baltimore’s best interest. Wieters went under the knife June 17, which might give him time to return by the start of next season, but the road back to the big leagues for the few catchers who had Tommy John surgery before the former fifth overall pick has been dark and full of terrors. Having Ruiz around would give the O’s a big assist this year and a strong safety net for 2015 in the event that Wieters’s comeback hits a snag. It would also give them the option to trade Wieters a year from now if it becomes clear that he and agent Scott Boras won’t sign an extension, or, alternatively, it would leave the O’s with the rights to an above-average backup if Wieters sticks around. Ruiz recently extended a six-season DL streak and will be 36 by the time he reports to spring training, so shifting to a backup role and getting some extra time off might be just the ticket to a productive tail end to his career.

Perfect Fit: OF Josh Willingham and SP Bartolo Colon and the Seattle Mariners

Closest Inanimate Object Equivalents: Starbucks cup + garbage can; Pumpkin + fruit basket

Why They Fit: The Mariners have received a lower collective OPS from their center fielders than any other AL team, and only the Astros have fielded less productive left fielders. The M’s need some offense in the outfield, and Willingham, whose recent slump may have lowered Minnesota’s leverage, would be a relatively inexpensive source. Safeco Field is still hard on right-handed power, but Seattle’s lineup leans so far to the left that Willingham would help just by breaking up same-handed hitters. However, he would hurt the Mariners’ MLB-best defense, whose massive improvement since last season has been the key to their success.

Meanwhile, though the M’s have one of baseball’s best rotation tops in Felix Hernandez and Hisashi Iwakuma, they’ve suffered from the lack of starting depth that recently pushed reliever Tom Wilhelmsen into a spot start. Beyond the two aces, they’re depending on Taijuan Walker’s command; James Paxton’s shoulder; Roenis Elias’s endurance; and Chris Young, a poor team’s Colon, to avoid an almost inevitable implosion. Adding Colon would leave a lot less to chance. As a fly baller who pitches to contact, the 41-year-old’s settings come pre-configured for defense-first teams with deep dimensions, so Seattle would make for a happy home. The only downside: In the AL, he’d rarely have to hit.

Perfect Fit: 2B Nick Franklin and the Oakland Athletics

Closest Inanimate Object Equivalent: Recycling bins + closet

Why He Fits: You wouldn’t think that a team with a plus-150 run differential could have a glaring weak spot, but only the Padres and Giants have gotten less firepower from the keystone than the A’s, whose ragtag band of second basemen have produced a .225/.285/.280 line. Now that the Cubs are hoarding Addison Russell inside their infield Fort Knox, Billy Beane has less prospect wealth to work with, but Franklin has A’s written all over him. He’s capable of playing both shortstop and second, and he’s a switch-hitter, so he appeals to Oakland’s love of platooning and defensive versatility. He’s also blocked by Robinson Cano and (evidently) Brad Miller, which might make him expendable from Seattle’s perspective. While some teams are reluctant to deal with close competitors, Beane has a history of completing intra-division trades. He wouldn’t hesitate to swing one more if Jack Z could be convinced.

Perfect Fit: 2B Ben Zobrist and the San Francisco Giants

Closest Inanimate Object Equivalent: Matryoshka doll + tea ball

Why he Fits: On Monday, the Giants signed Dan Uggla to a minor league contract, which is a good example of an imperfect fit. Uggla technically plays the position where San Francisco, which is locked in an NL West dogfight with the Dodgers, needs help, but his presence is more of a symptom than a solution. Considering the big-bicepped second baseman’s struggles in Atlanta, it would take the sort of luck/deal with the Dark Lord/scouting savvy that helped Brian Sabean strike gold with veteran castoffs Cody Ross and Pat Burrell in 2010 to make Uggla much better than the team’s existing alternatives, Joe Panik and a wizened Marco Scutaro, who’s much more hobbled than he was when Sabean may or may not have sacrificed several kittens to ensure he’d hit .362 for San Francisco in the second half of 2012.

Burrell is now a Giants special assignment scout, and one of his assignments is believed to have been scouting Zobrist. That checks out, because Zobrist, unlike Uggla, is the perfect fit San Francisco is seeking — not only because he’s the best second baseman available (assuming Chase Utley is determined to be a Phillie forever) and comes with an affordable option for 2015, but because he also plays outfield, an area in which the Giants could use additional depth. If the demand for Zobrist leads to too high a price tag (or the Rays reel off more wins and decide to stand pat), Sabean could try to pry Martin Prado away from the division-rival Diamondbacks. Although Prado isn’t Zobrist’s equal at present, he’s younger and plays third and left, which would give the Giants some leverage and flexibility as they prepare for contract talks with presumptive free agents Pablo Sandoval and Michael Morse.