The right-handed Cook utilized all of his pitches in a 22-pitch session Tuesday and is scheduled to throw even more in another bullpen session Thursday. At that point, the A's will decide whether he needs a rehab assignment before returning to the active roster.
"Today was great," said Cook. "It's one thing to be confident the whole time, but then to actually respond the way you feel is obviously a little relieving. Honestly I was thoroughly surprised with how good it was today, actually."
"He looked like he had never missed a beat," manager Bob Melvin said. "We feel like we dodged a bullet as far as what the injury looked like originally. He was going after every one of his pitches, throwing his slider as hard as he could throw it."
O'Flaherty, who will throw a simulated game in Sacramento on Thursday, said Tuesday he feels Major League-ready but understands he must remain patient with the process. The lefty hopes to make his A's debut in June.
"My arm's ready," he said. "It just has to get ready for that everyday grind.
"Everything feels great. It feels natural, pretty similar to how it felt before I even had the surgery. Where I'm at mentally, it's pretty good. When you first come out of surgery, the first four months, you don't doubt the process, but there are days when you're thinking, 'How am I ever going to throw again?' Now where it's at, I can't even tell I had surgery."
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.