He started the 2006 season with Lake County and with a .395 On-base percentage, earned a promotion to A-Advanced Kinston.

In what proved to be his last season in the Indians organization, he reached the highest level, Triple-A, with the Columbus Clippers.

On July 29, 2011, Constanza was called up to the majors when Nate McLouth was placed on the 15-day disabled list with a lower abdominal strain.

Two batters later, Braves first-baseman Freddie Freeman hit a sacrifice fly to drive in Constanza, netting him his first career run scored.

[3] On Sunday, August 7, 2011, Constanza hit his first home run in the top of the 5th inning against the New York Mets.

He was subsequently recognized for his odd habit of licking the hot spot of the bat after foul-tipping the ball.