With a cover by Neal Adams, Justice League of America #67 (November-December, 1968) was indeed a very special issue, as it showcased the cases that added members to the team.
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Carthan, the hero of the planet Dryanna, finds himself exiled from his home planet by its leader, Xandor. Ending up on Earth, Carthan finds the aura that gives him his invulnerability also prevents him from recruiting the JLA for help. So, instead, he kidnaps Green Arrow and unleashes menaces across Earth, tied to golden boxes that keep Carthan on Earth, hoping the JLA will destroy them, freeing him from Earth. While the other heroes stop the menaces, Superman and Batman try to free Green Arrow, but as the rest of the team arrives, all end up trapped in a giant diamond, and only Green Arrow's archery skills can free the team, which he does, allowing Carthan to return home to face his enemy, and Green Arrow to join the team. Green Arrow was more active in his next adventure (reprinted in the first JLA Giant), and with Snapper Carr, later learned the origin of the JLA (reprinted in an 80 Page Giant devoted to Secret Origins).
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The Atom wasn't the villain of the issue, in fact, though they voted him into the League unanimously, none of the Leaguers could remember who the Atom was. Green Lantern uses his power ring to search for information on the Tiny Titan, while Martian Manhunter heads to Ivy Town to find the diminutive hero (where, the citizens of the town, including the Atom, don't remember him either....). The villain behind this is "Mr. Memory", who used his De-Memorizer on them all, who also recruits Green Lantern foe Hector Hammond, Flash rogue Pied Piper, Aquaman menace Sea-Thief, Wonder Woman villain Angle Man and Green Arrow nemesis Dr. Davis to capture the team. Mr. Memory captures Martian Manhunter as he was approaching the Atom, who escapes by shrinking into a sub-atomic world, which restores the Atom's memory. The Atom follows Mr. Memory to his hide out, and is captured and nearly used as a weapon to kill the JLA members held captive, but they escape, capturing Mr. Memory....who is Batman! Batman had been captured off-panel by the Joker, had his memory messed with and used against the team, by the real villain of the piece, the JLA's foe, Professor Amos Fortune, whose first appearance was reprinted in the third JLA Giant.
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By this time, the team was getting so large, that even though they all voted Hawkman in (and, sadly, denied Hawkgirl membership by a "no similar powers clause", which held for years), only some of the members worked on Hawkman's first case. To be fair, it shouldn't have taken the entire League to stop small time crook Joe Perry, but nearly did. Still, Batman, Flash, Green Lantern, Wonder Woman and Hawkman first fought crooks using odd hoops that transported them into the future, and, after stopping them, headed back to their Secret Sanctuary to analyze the case....only to find themselves and part of their HQ thrown into space. All because of Joe Perry and an alien device that he found, which allowed him to manifest his thoughts, who then came up with the "Super-Duper", a being with Batman's torso, Wonder Woman's head and lasso, Flash's legs, Green Lantern's arms and power ring, and Hawkman's wings to battle the team. Hawkman figured out a way to defeat the composite menace and its master, ending his induction to the League.
Black Canary and Elongated Man) as charter members like Wonder Woman and Martian Manhunter went on leave, as well as have more Giant issues though the issues wouldn't be quite as giant either!