They think Huston Street fits that tradition, which is why the team announced Sunday it has agreed to a two-year contract extension with Street worth $14 million, with a club option for 2015.
"It's an honor," Street said. "To be a part of those guys, I still think I got a lot of work to do. I think you look at what Heath had done, what Trevor had done, obviously. Trevor is one of the greatest closers of all time, if not the greatest closer. Certainly it's a role I take very seriously, and I want to continue to do it at a level of excellence like those guys did for so many years."
Street will make $7 million in each of the next two seasons. The Padres own the club option that's worth $7 million for 2015. There are no buyouts or incentives in the deal, which Street said he "absolutely" set the terms of during negotiations.
"I would think I probably gave up some [money]," Street said. "Some people might say it's a team-friendly contract. That's fine with me. I'm happy. It's friendly to me. It's going to be very friendly to me."
Street is making $7.5 million this season as part of a contract extension he signed while with the Rockies on Jan. 27, 2010. He had a $9 million player option for 2013 that the club had the option of declining.
But the Padres -- who obtained Street and cash from Colorado on Dec. 7 for Minor League pitcher Nick Schmidt -- quickly became enamored with Street's ability to handle the ninth inning.
"Huston has done a fantastic job for us, and he's fit our clubhouse well," said Padres general manager Josh Byrnes. "He's about to turn 29 [on Thursday]. We think this is a good decision to solidify the position for us."
In his first season as closer for the Padres, Street -- who earlier this month represented the team on the National League All-Star roster -- has converted all 17 of his save opportunities with a 0.91 ERA in 31 appearances. He's allowed 11 hits in 29 2/3 innings and currently has a scoreless streak of 15 innings.
"This game is about performance, and as a Padre, he's performed well," manager Bud Black said. "He'll be the first to tell you he wants it to continue, as do we.
"He's a perfectionist in a lot of ways, so he's still trying to refine his game to get the most to maximize his ability."
Street missed 29 games this season with a strained right lat muscle, but has gone 2-0 with a 0.90 ERA and 13 saves since coming off the disabled list June 5. He's limited opposing hitters to a .119 batting average over that stretch.
Street made it clear earlier this month that he likes the direction the team is going with so many young, promising players on the roster, and that he wants to be part of it moving forward, something he reiterated Sunday.
"The organization itself is a bunch of people that I like, that I like being around, that I want to go play for, and ultimately you have to believe in that, you have to believe in everybody involved," Street said. "Like I told Buddy and the rest of the coaches, I wouldn't have signed this if I didn't believe in you guys, if I didn't believe in the rest of my teammates.
"I thought [free agency] would be exciting, but when you have a chance to avoid it and do something you want, you have to take advantage of that. I was thankful the Padres gave me that opportunity."
Street becomes the second potential trade target the Padres have taken off the table in the last week. On July 22, the team signed outfielder Carlos Quentin to a three-year extension for $27 million.
"It says a lot that two well-respected players that have been on a couple different teams have made a commitment to our organization," Black said. "I think that should make everybody feel good -- players, coaches, front office, fans. I think it signals a lot of positive things."
Added Street: "We were up against the deadline. I knew if we didn't get something done by [Tuesday's non-waiver Trade Deadline], there was a pretty good chance I wouldn't be here. I knew where I wanted to be. I knew where my first choice was, and I got that done."
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. Associate reporter Tom Green contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.