Miami — Left-hander Tom Glavine and Mike Hampton were encouraged by progress when they each threw a bullpen session Tuesday at Dolphin Stadium, and Hampton thinks he could be back by next week.

Glavine is recovering from a flexor-tendon tear near his pitching elbow and Hampton a strained groin. Glavine hopes to return to the rotation by mid-August.

Hampton hasn't pitched in a major-league game in 35 months, sidelined by an array of injuries and two elbow surgeries. This year's ailments: a strained (and re-strained) pectoral muscle and the groin strain, which occurred July 16 in what was to be his final minor-league rehab start.

"Felt really good," Hampton said after Tuesday's 35-pitch session. "I threw everything. I didn't overdo it, threw with pretty good velocity, let a few go."

He said he would throw another bullpen Friday and hoped to be activated if that session goes smoothly.

"I've got to test it, go at max effort, then see what they want after that," he said, adding that he doesn't need any more rehab games. "I told them I was ready. That's my personal opinion.

"My arm feels good. I told them if I can get through this next bullpen session, let's do it [activate him]."

Glavine, 42, hasn't pitched since June 10. Saturday, he threw his first bullpen session since the injury, at about 60-percent effort.

He ramped it up to 75-80 percent in a 40-45 pitch session Tuesday.

"It felt better today, felt like I had a little bit more arm strength," he said. "It felt like the ball was coming out of my hand better today, the ball had a little more zip on it and [his shoulder] didn't feel as cranky. All those are good signs."

Glavine said in recent weeks the shoulder was a little sore from the loss in arm strength during his down time.