Pineiro was placed on the disabled list retroactive to May 21, so he would have been eligible to be activated on Thursday -- if he were healthy enough to pitch. He's not, though, so he will be skipped again.
"He hasn't made that much progress," manager Tony La Russa said.
Parisi fared well in eight relief starts after he was called up from Triple-A Memphis to take Anthony Reyes' spot on the roster. However, he was shellacked in his first big league start, allowing eight runs in 2 2/3 innings. He'll get another chance, on Thursday at Washington.
In six starts for Triple-A Memphis this year, Parisi went 2-1 with a 4.41 ERA, 23 strikeouts, 13 walks and two home runs allowed in 32 2/3 innings.
Matthew Leach is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.