ACTION COMICS 335 (March 1966)--2nd story, "The Prize of Peril" by Binder and Mooney
ACTION COMICS 336 (April 1966)--2nd story, "The Forbidden Fortress of Solitude" by Binder and Mooney; cover art by Swan and Klein:
Linda Lee Danvers again seems obsessed with glamour over heroism when she competes for the crown of Miss Universe; however, on this occasion she has a secret purpose.
Through an alien probe sent to Earth, Linda learns that the seemingly innocent beauty contest is really a scheme to bring women from different planets to compete for that year's Miss Cosmos crown.
Linda covertly uses her super-powers to win the Miss Universe title for Earth, upon which she's abducted to the world where the Miss Cosmos contest is held annually. The master of the contest, Jak-Thal, says that the winner of Miss Cosmos will never want to return to her homeworld.
There, Supergirl is attended by servants who hide their faces behind bandages.
Against the other contestants, the Midvale Marvel easily wins the crown and the grand prize--the Eternal Cabinet of Youth--which she must sleep in that night. The Eternal Cabinet is supposed to confer ever lasting youth, but during the night the servant women try to rescue Linda from this pod. They were all previous winners of Miss Cosmos and as the servant Zilya reveals, their faces were horribly disfigured after sleeping in the Eternal Cabinet.
Jak-Thal blasts the women and then reveals his true face which was deformed on a trip through space by the radiations of a spiral nebula. Supergirl defeats him handily, but upon returning to Earth, she finds that her face has become distorted.
In the next issue, the self-conscious Kryptonian heads off a collision between the Bizarro World and another planet, but the Bizarros make a duplicate of Supergirl that has Linda's regular face--although this Girl of Steel has a Bizarro brain.
The beautiful Bizarro goes to Earth, where she takes charge of the Super-Horse and bars Superman from the Fortress of Solitude.
Jak-Thal, having seen the error of his ways, sends a Miss Cosmos crown to Supergirl that restores her natural beauty.
Note: "The Great Miss Universe Contest," in SUPERMAN’S PAL, JIMMY OLSEN No. 83 (March ’65), also was a ruse for nefarious purposes--see post #69.