CINCINNATI -- The long, anticipated return of Jack Flaherty finally has a light peeking out towards the end of the tunnel.

The right-hander will pitch in a rehab game for Triple-A Memphis on Tuesday, manager Mike Shildt said prior to Saturday’s game against the Reds, marking both his first game action and his first time facing live hitters since suffering the oblique tear on May 31.

Most impressive -- and positive: Flaherty will be on a pitch count of 40 to 45, Shildt said, which is a far higher mark than initially expected.

For context: Miles Mikolas, who’s been thought to be a couple steps ahead of Flaherty in his own return from a forearm injury, was slated to throw as many pitches in his first rehab stint with Memphis on Saturday. Mikolas faced live hitters thrice before hitting rehab, too.

Perhaps a splashy opening act on the surface, the Cardinals will exert extreme caution with Flaherty, their 25-year-old ace, and especially with how he comes out of his first couple rehab outings. Still, the fact that Flaherty finds himself back in game action before the end of July is impressive in its own right, setting up a return in the second half of August if all goes off unhampered.

“He’s a tunnel-vision guy,” Shildt said. “He goes, ‘I want to get my next.’ We'll check the box and move on.”

Part of what has allowed Flaherty to start his rehab with this workload is the nature of his oblique injury, which, hitting him on the left side, allowed him to keep his right arm in decent shape throughout the process. That started with simple step-and-throws, continued with playing catch and ended with a side session on Saturday -- his final hurdle before taking a trip to meet Memphis.

“He’s Jack,” Shildt said, alluding to how refined he has been throughout this long process. Shildt also confirmed that “he’s definitely jacked as well” with his rehab progressing.

And so are the Cardinals.

Cards go over for one remaining pick

The Cardinals’ signing of Alec Willis, their seventh-round pick from the 2021 Draft, on Saturday signaled not just the nearing of the end in signing their entire Draft class, but another commitment to sway a young, talented player away from their college commitment.

• Cardinals Draft Tracker

MLB Pipeline’s Jonathan Mayo reported that Willis, a right-hander out of Regis Jesuit (Colo.) High School, signed for $1 million -- well over the $211,500 slot value of the 211th overall pick. (The club did not confirm the figure.) That was necessary to sway the pitcher away from his commitment to the University of Minnesota, and it resembled the fifth over-slot deal the Cardinals made in this Draft, aided by under-slot deals elsewhere, most notably with their first-round pick in right-hander Michael McGreevy.

The Cardinals were already reaching when they selected what became their two biggest over-slot deals -- Willis and second-round pick Joshua Baez, a power-hitting outfielder committed to Vanderbilt. Willis was the No. 130 ranked prospect in the Draft per MLB Pipeline; Baez was ranked No. 24 and selected 54th overall.

But contract in hand, both now inject some high-caliber youth into a St. Louis pipeline that is rather top-heavy. Both forewent blue-chip schools to start their careers as Cardinals.

St. Louis has just two remaining Draft picks unsigned -- outfielder Elijah Cabell (Florida State, 17th round) and third baseman Xavier Casserilla (V.R. Eaton High School in Texas, 20th round).

Bird droppings

• With Yadier Molina (stiff neck) unavailable after his scheduled off-day on Friday, Saturday’s contest marked just the first time since June 6 that Andrew Knizner started in back-to-back games, when Molina was dealing with a knee contusion. Friday was just his fifth start since the start of June -- though he didn’t look as such with a 2-for-4 night, including a two-run double.

“He’s an impressive guy, too, because he's staying sharp,” said Shildt, noting the extensive video work Knizner did in the offseason. “ … It’s a continuation.”

• Speaking of the Redbirds … maybe time to break them up? With a 4-1 win on Friday, Memphis rattled off its 13th consecutive victory -- a franchise record -- with an MLB pitcher helping them go for No. 14 on Saturday. And if the winning keeps up, Flaherty could help them with 16.