"They're in our division, they're second behind us, and that's why we need to put them away," Hancock said of facing his old club. "Personally? No, I've played for other teams, and I wish [the Reds] all the best."
Hancock, 28, was a starter in Cincinnati, but he has adapted to pitching out of the bullpen. He has posted a 2.25 ERA over his last 10 outings, eight of which have been scoreless efforts.
"He's done a variety of jobs really well," Cardinals manager Tony La Russa said of Hancock. "He's also been effective against right and left. ... For a while there, he was our best with inherited runners. He's stayed healthy, can pitch often. ... He's done a good job for us."
After enduring a rough June (2-1, 5.54 ERA), Hancock has posted a 3.27 ERA with one save during July and the first four games in August.
"I just go out there and do my job," Hancock said. "All I can hope for is the best. I didn't envision it happening like this, but it's been a wild ride and it's been a fun ride. I've enjoyed it."
No matter how Hancock may have exited the Reds organization, La Russa has nothing but praise for his young right-hander.
"From the first day until now, he's been a pro," La Russa said.
Mulder madness: Cards right-hander Mark Mulder will make his second rehabilitation start in the Minors at Triple-A Memphis on Friday.
If all goes well and his shoulder keeps improving, he could rejoin the rotation some time next week.
"Mulder at his best would be huge," La Russa said. "At his nearly-best would be very good. We'll see what happens after Friday [and] continue to move forward."
Lineup changes: With the Reds starting left-hander Eric Milton, La Russa started So Taguchi in place of Jim Edmonds in center field on Tuesday night.
Edmonds has struggled against lefties this season. He is batting .170 with three homers and 12 RBIs. Against right-handers, he is hitting .295 with 13 homers and 47 RBIs.
"Right now, here's a guy that left-handers are doing real well against," La Russa said of Edmonds. "Why would you push him? Not unless he's red-hot or something. [There] isn't anything wrong with guys not wearing down."
After a rare day off, David Eckstein returned to the leadoff position and shortstop. La Russa stacked the batting order with seven right-handed bats and Scott Spiezio, a switch-hitter, started in left field.
Miles-stone: Aaron Miles was a bit anxious during much of Monday night's opener.
Miles, 29, is in his third Major League season, but he made his first start at shortstop to give Eckstein a day off, and it took a while for the first ball to be hit to him.
Not until the seventh inning, when Miles helped turn a 6-3 double play, did he get his first opportunity.
"I was waiting to get my feet wet, and it took until the seventh inning," Miles said, laughing. "Just happy to get a win, and get out there and give Eck a day off."
In his first year with St. Louis, Miles' versatility helps make up for the loss of Hector Luna, whom the Cardinals traded to the Indians for second baseman Ronnie Belliard.
"It's neat, it keeps you on your toes." Miles said of his temporary position switch. "La Russa is one of those managers that believes in his players. It feels good to get my name penciled in there for a start at shortstop, and I'll be ready for when it happens again."
On deck: A pitching duel highlights the third game of a four-game series between the Cardinals and the Reds on Wednesday at 6:10 p.m. CT at Great American Ball Park. Cards righty Chris Carpenter takes on Reds 12-game winner Aaron Harang.