KISSIMMEE, Fla. -- The stretch run begins Tuesday.

The Phillies beat the Astros, 7-1, in a Grapefruit League game Sunday at Osceola County Stadium. They do not play Monday, giving them 18 games before they open the regular season April 1 in Atlanta.

Those 18 games will decide the makeup of the seven-man bullpen.

"In my mind, there are three jobs available," pitching coach Rich Dubee said.

Dubee said last week the competition for those jobs begins Tuesday, almost discarding previous appearances as pitchers tuned up their deliveries and pitches the first few weeks of camp. Jonathan Papelbon, Mike Adams, Antonio Bastardo and Chad Durbin are guaranteed spots in the bullpen. The other three jobs are up for grabs, with right-handers Phillippe Aumont, Justin De Fratus and Mike Stutes joining left-handers Jake Diekman, Jeremy Horst and Raul Valdes in the pack.

Are their front-runners at this point?

"There are guys that are ahead of other guys, yes," Dubee said.

Dubee would not mention their names, but general manager Ruben Amaro Jr. has indicated a couple times in the past week that Aumont is slightly ahead of the rest. Aumont has allowed one hit and struck out two in two scoreless innings in two Grapefruit League appearances. He pitched for Canada in the World Baseball Classic, where he allowed three runs (on five hits and one walk) in 1 2/3 innings. The Phils love his arm and potential.

Finalizing the remaining three relievers will come down to various factors.

"I don't disregard what they did last year or track records by any means," Dubee said. "Those are important. But I also have to see a guy pitching close to what I've seen in the past. If some guy lights it up, you can't discount that."

Horst and De Fratus pitched Sunday. Horst has had a rough spring, but he struck out two in a scoreless eighth inning. He entered the afternoon with a 14.40 ERA in four appearances, but he went 2-0 with a 1.15 ERA in 23 appearances last season with the Phillies. De Fratus was 1-0 with a 9.00 ERA in four appearances before striking out one in a scoreless ninth inning on Sunday. He had a 3.38 ERA in 12 appearances last season.

The Phils have said they will take the best pitchers for those final three spots, regardless if they are right-handed or left-handed, but they certainly would like one of them to be left-handed. That means Diekman, Horst or Valdes could go in that spot. Diekman has a 3.00 ERA in five appearances, striking out 10 and walking two in six innings. Diekman's Achilles' heel is his command. He walked an alarming 20 batters in 27 1/3 innings last season. If Diekman can throw more strikes, his chances to make the roster improve.

"I would say so," said Dubee, asked if Diekman's command has improved. "He's still getting behind too many guys or not finishing guys, like you'd like to see when he's got them 0-2 and stuff. But yeah, I think his ability to get back in the strike zone is coming back. If he misses, he gets back into the strike zone."

Valdes is 35, so he does not fit the profile of the other pitchers in this competition because he is not considered a prospect, but he went 3-2 with a 2.90 ERA in 27 appearances last season. He has a 7.36 ERA in four appearances this spring.

Aumont, Stutes and De Fratus are the top right-handers in the hunt. If Aumont is a front-runner, Stutes and De Fratus are not far behind. Stutes impressed in 2011, when he essentially bailed out a depleted bullpen that suffered injuries to Brad Lidge, Ryan Madson and Jose Contreras. Stutes went 6-2 with a 3.63 ERA in 57 appearances that season, but a shoulder injury forced him to miss most of last year. The Phillies have long liked De Fratus' potential.

Stutes has pitched better recently after struggling in his first two spring appearances.

"I know it's impossible not to think about that kind of stuff," Stutes said late last week. "But I really try to not sit there and watch what everyone else is doing: 'Am I doing better than him? Is he doing better than me?' [The coaches and the front office] are the only ones that know that stuff. It's tough. From our perspective, I've come to the realization that I just need to go out there and do everything I can. Put yourself in a good situation and hopefully they think you're doing a good job and they want to keep you around. That's the attitude I'm taking toward it."