NASHVILLE, Tenn. — A few years ago, Dave Dombrowski wouldn’t have made the trade he pulled off yesterday.

“Before, if you had a closer and you had a set-up guy, you were probably pretty well established in building a bullpen the best way you can,” Dombrowski said. “I know for myself, if you said, ‘You’ve got (Craig) Kimbrel, you’ve got (Koji) Uehara, (Junichi) Tazawa and some young guys,’ you would say, ‘Oh, great.’ ”

But the game has changed. Deep, dominant bullpens are all the rage now, teams realizing they can shorten a game to six or seven innings and while putting less pressure on their starting rotation if they’re able to roll out wave after wave of relievers with power stuff and a variety of arm slots.

Call it the Kansas City Royals Effect.

And after years of building contending Detroit Tigers teams that fell short because of inadequate bullpens, Dombrowski is adapting. Three weeks after trading for Kimbrel, the Red Sox president of baseball operations struck quickly on the first day of the winter meetings by acquiring 26-year-old set-up man Carson Smith in a four-player trade with the Seattle Mariners.

In a classic case of trading from a surplus to fill a need, the Red Sox received Smith and depth starter Roenis Elias in exchange for starter Wade Miley and reliever Jonathan Aro. And while we can debate whether the Sox would have been better off trading Clay Buchholz or even Joe Kelly than the durable, dependable Miley, there’s no denying they had a greater need for a reliever like Smith than an innings-eating, back-end starter who had been rendered superfluous after the $217 million signing of ace David Price.

“Miley did a nice job for us,” Dombrowski said. “Any time you get a guy that pitches well, wins double-digit games, pitches close to 200 innings pitched and does a lot of things that help you, sure it is (tough). But we also knew we probably had too many numbers and we still had depth, and it was a way for us to improve our bullpen.”

Indeed, the Sox suddenly possess a group that, health-permitting, could rival any back-of-the-bullpen combination in baseball. While the ninth inning belongs to Kimbrel and the eighth to erstwhile closer Uehara, the addition of Smith gives manager John Farrell a late-inning alternative whenever 41-year-old Uehara or overused Tazawa require a rest.

Farrell’s eyes lit up like the Citgo sign when he began to consider the options in his new-look bullpen.

“Much deeper,” Farrell said. “What’s clearly different with this group is it’s deeper in talent, it’s deeper in performance and it’s deeper in the ability to get strikeouts in key spots.”

In his first full big league season, Smith posted a 2.31 ERA and 13 saves in 17 chances after taking over in midseason for ineffective closer Fernando Rodney. Smith’s average fastball velocity dipped slightly from 91.5 mph in 2014 to 90.5 mph in ’15, but the deception in his three-quarters delivery, heavy sink on his fastball and nastiness of his slider have the Sox confident there isn’t any cause for concern.

Farrell called Smith “everything we hoped to get in a reliever” and compared him to Jeff Nelson, who slung the ball from a similarly low arm slot en route to years of effectiveness in a late-90s New York Yankees bullpen that included closer Mariano Rivera and fellow set-up men Mike Stanton and Ramiro Mendoza and was the precursor to the World Series champion Royals’ shutdown bullpens with the likes of Wade Davis, Kelvin Herrera, Greg Holland and this, year, Ryan Madson.

Assuming Uehara holds up and Tazawa bounces back after a rough second half of 2015, the Red Sox believe they have a group capable of dominating the late innings.

More importantly, they have coverage in case Uehara or Tazawa falters.

“We’re a lot deeper out there,” Dombrowski said. “When John wants to rest people, he can move people up a notch. If he wants to rest Kimbrel, he’s got Uehara. If he wants to rest Uehara, he’s got Tazawa and he’s also got Smith.”

The Red Sox were fielding calls on their starters for several weeks, but talks picked up over the weekend after Price’s deal became official. The Sox could have sold low on injury-riddled Buchholz or given up on Kelly’s upside. But Miley was attractive to starter-needy teams, including Seattle and the Miami Marlins, because of his age (29), durability (average innings-pitched of 198 over the past four years) and the fact that he’s relatively affordable ($15 million due over the next two seasons) at a time when back-end starters such as J.A. Happ are signing for $13 million per year (Toronto Blue Jays).

And when the Mariners were willing to trade Smith, who is under club control through 2020, the Red Sox jumped at the chance. After all, Dombrowski has learned the hard way that he can never have enough capable relievers.

“I wouldn’t downplay the success of Kansas City and how good they’ve been,” Dombrowski said. “I think it shows the more guys you can keep trotting out there the better off you are. Adding that one more arm out there really gives you that much more comfortable feeling. Because if somebody does get hurt, you’ve got that.”

Now, at last, the Red Sox can say they do.