SAN FRANCISCO — Left-hander Erik Miller took another step towards recovering from his left elbow strain on Tuesday, throwing his second bullpen since going on the injured list earlier this month.

Miller threw exclusively fastballs at about 75% effort during his 20-pitch bullpen session this past Saturday, but he incorporated his full gamut of pitches during his bullpen session on Tuesday.

“It’s obviously something you want to mess around with,” Miller said of his injury. “I’m just happy that I took a couple weeks off and it’s feeling pretty good.”

Manager Bob Melvin said the team will see how Miller feels following the bullpen, then determine the next steps from there. Miller, who hasn’t pitched in a game since July 2, hopes to make several rehab appearances before returning given how long he’s been sidelined.

“My preference is to throw at least two — maybe even three — (rehab outings) because, at that pint, it would have been over a month since throwing in game,” Miller said. “At this point in the year, it’s too important to try to knock the rust off up here. Whether it’s Sacramento or San Jose, we haven’t thought that far ahead, but I’d like to throw a couple.”

Miller, 27, has been an integral part of the Giants’ bullpen, posting a 1.50 ERA (3.92 FIP) over 30 innings. In Miller’s absence, Newark native Joey Lucchesi and Matt Gage have served as Melvin’s left-handed options out of the bullpen. Lucchesi has a 1.65 ERA and hasn’t allowed a run in July, while Gage hasn’t allowed a run since joining the Giants.

“Both of them have done a great job,” Melvin said. “Gage even opened for us, did a nice job against a pretty good top of the (New York Mets’) lineup. He’s pitched well, and so has Lucchesi. Lucchesi’s done multiple innings for us and faced righties.”

Along with Miller, right-hander Landen Roupp threw off flat ground for the first time since being placed on the injured list with right elbow inflammation.

Roupp, who was placed on the injured list on July 25 (retroactive to July 23), will travel to Arizona to continue his rehab once the Giants travel to the East Coast for their two-city road trip against the New York Mets and Pittsburgh Pirates. The Giants expect Roupp’s injury to be on the minor side, and it’s possible he spends the minimum amount of time on the injured list.

“He hasn’t been out too long, so hopefully, we can get him back sooner than later,” Melvin said of Roupp, who has a 3.11 ERA over 20 starts.

Melvin pays respects to Sandberg

Hall of Fame second baseman Ryne Sandberg, who spent 15 seasons of his major-league career with the Chicago Cubs, died on Monday at the age of 65.

“What a great player and what a great guy and how he would give back to the game,” Melvin said. “I think there were heavy hearts everywhere in baseball. Certainly last night and certainly today.”

Sandberg, known for his combination of power, speed and defense, finished his career with nine Gold Glove Awards, 282 home runs and 344 stolen bases. His list of accolades also includes the 1984 NL MVP, seven Silver Slugger Awards and 10 All-Star selections.

“You just felt like whenever the wind was blowing out at Wrigley and he was up, there was a good chance it was going to be a homer,” Melvin said.

Giants sign former Dodgers top prospect

Catcher Diego Cartaya, who was once considered one of baseball’s best prospects with the Los Angeles Dodgers, has signed a minor-league contract with the Giants, per Daniel Álvarez-Montes.

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Cartaya, 23, was considered the top international prospect of his class when he signed with the Dodgers out of Venezuela as a 16-year-old in 2018. MLB Pipeline still considered Cartaya as a top-20 prospect as recently as 2023, but he struggled in the upper levels of the minors.

In January, the Twins traded for Cartaya after he was designated for assignment by the Dodgers. On July 23, Minnesota released Cartaya after he had a .353 OPS over 20 games with the Twins’ Triple-A affiliate.