The man from Australia has put together six scoreless two-hit innings, with no walks while striking out six hitters. His spring ERA is at 3.86.
Thompson finished a victory over the Cubs on Friday with two strong innings, catching Josh Kroeger looking at a third strike to notch the save.
"That was a great hook he threw 3-2 [in the count]," pitching coach Mike Butcher said with approval.
Bulger, 29, made his fourth Cactus League appearance on Tuesday against the Brewers, walking one man and striking out a pair to finish an 11-4 win with a scoreless ninth. It's all about command with the hard-throwing Georgian who was a first-round pick (22nd overall) by Arizona in the 2001 First-Year Player Draft.
"Throw strikes, quality pitches -- in and out and get it down," Bulger said of his mission. "It's night and day from last year, when I was coming back from a shoulder injury."
Bulger, whose spring ERA is 7.20 in four appearances, fashioned a 2.84 ERA in six games for the Angels last September. Thompson had a 10.80 ERA in seven outings.
The remnants of a blister on his middle pitching finger that briefly sidelined him are visible, but Thompson has found his rhythm and form.
"The first time out I was kind of working out the kinks," Thompson said. "I can only do what I can do. It's up to them. If I keep putting up zeros, I'll definitely give myself the best chance possible."
O'Day, whose down under delivery has been an over-the-top successful this spring, worked two innings against the Brewers, with one of the two runs he allowed unearned. He is 3-0 with a 1.35 ERA.
Serrano, a 27-year-old Venezuelan, is 1-1 with a 1.86 ERA in six Cactus League games, striking out six with one walk in 9 2/3 innings.
"It's right there in front of a lot of guys," Butcher said. "We have strike throwers, guys with good stuff. We'll have to play it out, see what happens."