But as for three of their starters who actually are on the shelf, their status is still a bit hazy, as manager Joe Maddon said there is still no timetable for the return of shortstop Jason Bartlett, designated hitter Pat Burrell and left-hander Scott Kazmir.
Burrell, who has been out since May 11 because of a neck strain, was eligible to come off the 15-day DL on May 26, but he has hit a bit of a roadblock in his recovery. Maddon said the 32-year-old hit off a tee Wednesday and will do so again Thursday before taking live batting practice while Tampa Bay is on the road.
Once the Rays get back from their four-game trip to New York on Tuesday, they'll set up a schedule for Burrell to partake in some Minor League rehabilitation games -- if everything is fine.
Things are also a bit unclear for Bartlett, who's missed eight games because of a left ankle sprain.
The 29-year-old -- who is still leading the Major Leagues with a .373 batting average -- is eligible to come off his DL stint next Wednesday. But Maddon said he's still not sure if that will happen.
"I don't know that answer," Maddon said. "I just know that he's feeling better.
"[The ankle is] still sore, but he's getting better. Again, there's no definitive insight or finish line with him, but it's getting better. ... He's been moving around a little bit. He was moving around a little bit [Wednesday], and [head athletic trainer] Ron [Porterfield] said it came out good."
Kazmir, who is dealing with mechanics issues while recovering from a right quadriceps strain, threw another bullpen session Wednesday and said it went well.
The 24-year-old will continue to throw in the 'pen, with a couple of days off in between, for about a week. Then, if all is well, he will perhaps see if he can map out a schedule to pitch in a few rehab games.
"Every day it's feeling better," Kazmir said. "I'm just getting a better path to the plate, staying closed more. I'm throwing long toss every single day, and it's really helped."
Maddon still has no timetable for the lefty's return, but he likes Kazmir's current throwing program, which he said would allow him to repeat his arm slot more consistently and, in turn, have better command and velocity on his fastball.
For now, Kazmir's rationale is just like Maddon's -- day-to-day.
"I don't want to set a date -- I really don't," said Kazmir, who's at least expected back before the All-Star break. "That's not what we're trying to do here. We're just trying to go until everything feels perfect, everything feels right, and then hopefully never look back after that. That's the goal we're going for, and then hopefully we'll stick to it."
Alden Gonzalez is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.