The Corellian Cross was an award given to Rebel Alliance pilots and existed since the inception of the Rebellion until the inception of the New Republic. The award commemorated the signing of the Corellian Treaty, which marked the birth of the Alliance.
The award parameters have always been, "Any person serving in any capacity in the military, who has distinguished themselves in action with the military, or in operations conducted with friendly foreign forces, by taking extraordinarily heroic action at the risk of life sufficient to set the individual apart from his or her comrades."
This award is often given in lieu of another, higher award which was not appropriate, or when the action or actions was thought insufficient for a higher award.
Recipients included Ace Azzameen and Keyan Farlander, the latter for his role in capturing the warheads used to destroy the Imperial-class Star Destroyer Invincible (which effectively put an end to Operation Strike Fear).