His appearances are rarely uneventful.
That includes Tony Reagins, the Angels' general manager.
"I'm human too, so nerves come into play," Reagins said.
"It may not be pretty all the time, but the results are there -- and that's what we're looking for on a nightly basis, the end result."
Rodriguez has gotten the desired result more often than any closer the last three years, recording 132 saves in that span.
But he may take his tightrope act elsewhere after this season, when the $10-million contract he was awarded in arbitration is over and he can test the free-agent market.
Last winter -- and even last month -- the Angels could put up a good argument for letting him go.
Closers with lesser credentials than his got crazy money during the off-season: Minnesota kept Joe Nathan with a four-year, $47-million deal, and Cincinnati gave Francisco Cordero a four-year, $46-million contract. Rodriguez would be justified to ask for even more.
And when he got off to a shaky start this season, plagued by sore ankles and blowing a save against Cleveland on April 7, letting him depart didn't seem like such a bad idea.
Although Rodriguez wasn't needed in the Angels' 6-1 rout of the Oakland A's on Wednesday, he ended the month with more confidence and better numbers than seemed likely a few weeks ago.
The Angels may look at their budget and say they can't afford to keep him.
In reality they can't afford to lose Rodriguez, who has developed an effective slider and polished the changeup he brought out last year to the point where it's a reliable out-pitch.
Over the winter they offered him a three-year deal for a reported $34 million, and he declined. Reagins said Wednesday the two sides had "kind of tabled things" but didn't close the door on seeking common ground later.
"We know what he brings to the table, what he had done for our organization and our club over the years. So that part of it is not a concern," Reagins said. "It's just a matter of working out things.
"He's young. I think youth is on his side. You never know in this game. Injuries are always a part of the picture but when youth is on your side, I like youth."
Rodriguez has essentially grown up here. The Venezuelan-born right-hander is now a father of three, stockier than the whippet-thin kid he was in 2002 when he blew batters away and became the youngest pitcher to win a World Series game at 20 years, 286 days.
He wants to stay with the organization that signed him four months before his 17th birthday.
"Of course, of course," he said. "But it's not up to me.
"Remember, this is a business. There are things I can't control. We'll see. I can't predict the future."
He's doing his part, focusing on pitching instead of campaigning for a new contract.
Since his first four appearances, in which he threw more balls than strikes (35-32) and squandered a lead over Cleveland, he has appeared in one non-save situation and had eight save opportunities, converting all eight.
In his last 7 1/3 innings he has given up four walks and four hits, three of those hits to Kansas City on April 17. He hasn't given up an earned run since that game and hasn't yielded a hit in his last four outings. His earned-run average, which had ballooned to 8.31 on April 13, is down to 3.86, and he leads the American League with 11 saves.
"I'm feeling a lot stronger now and I know the more I get into the season the better I'm going to be feeling," he said.
"I'm feeling more comfortable. I made some changes in my mechanics, in my delivery, and it takes some pressure off of my ankle. I feel like I'm getting back to where I need to be."
The changes were designed to ease the stress on his left (landing) foot and end his habit of falling all over the mound on his follow-through.
"If you want to be in this business for a long time, you have to make some adjustments," he said. "I'm 26 years old but I've already been six years in the big leagues. I've got to make sure my body can be comfortable with it if I want to play in the big leagues for a long time."
It's to his credit that he hasn't become distracted by thoughts of the huge payday that lies ahead for him, whether in Anaheim or somewhere else.
"He's too strong-willed," pitching coach Mike Butcher said. "This guy's got one thing on his mind and that's winning a championship, winning games, saving games. I know that's what his goal is.
"He's a professional. . . . I think the rest of the stuff ends up taking care of itself after he takes care of what he has to do here."
It's up to the Angels now to take care of him and keep him here.