Alldred was designated for assignment by the Pirates on Tuesday.
Alldred had his contract selected May 11 and delivered a scoreless frame in his MLB debut before being demoted two days later, and he's now been removed from the Pirates' 40-man roster. The 25-year-old has pitched well for Triple-A Indianapolis this season with a 1.33 ERA, 1.04 WHIP and 17:6 K:BB across 20.1 innings.