The short opens with Sylvester once again attempting to catch Tweety, this time succeeding and closing the blinds to hide the evidence. Before he can eat Tweety, however, he is interrupted by a crimson, erudite, milquetoast cat (named "Clarence" or "Sam" in some sources but unnamed in the short itself), who tells him that his constant cravings for Tweety are a sign of profound personal weakness, and that the only way for him to overcome this weakness is to kick the habit for good. Believing that he is in need of help, Sylvester proudly joins "Birds Anonymous", a group of cats who have banded together to overcome their addictions to birds. Sylvester lives by this motto: "Birds is strictly for the birds!"
However, Sylvester's resolve begins to break down after a short time, primarily due to constant temptation since he still lives in the same house as Tweety. The temptations begins to grow even more after he hears TV commercials featuring a stuffed turkey and bird-themed songs on the radio. Sylvester valiantly makes many attempts to control his baser urges, even physically chaining himself to a radiator at one point. After Tweety asks the cat: "Don't you wike me anymore?" Sylvester replies: "I think... I think... I think you're... I think you're... DELICIOUS!" and makes another grab for Tweety, only to be stopped by his cat friend again.
Sylvester is unable to sleep that night, and eventually gives in to his basic instincts to try to grab Tweety, but is stopped again when his cat friend pours alum in his mouth. Sylvester then attempts to literally drink Tweety through a straw but fails. Ashamed of his weakness, Sylvester collapses into sobs ("I can't stand it! I gotta have a bird! I'm weak! I'm weak, but I don't care! I can't help it! After all, I am a pussycat!"), but the cat friend consoles him, telling him severe withdrawal symptoms are all part of the process, and that if he stays with the "Birds Anonymous" program, he will eventually succeed and come to love birds, as he does. However, when the cat kisses Tweety to prove his point, years of his denial take their toll and the B.A. cat attempts to devour Tweety himself, this time with Sylvester restraining him and telling him to control himself.
Tweety, escaping to a nearby counter, watches and sums up the whole affair with a shrug: "Like I said before: Once a bad ol' puddy tat, always a bad ol' puddy tat!"
Birds Anonymous won the Academy Award for Best Animated Short Film in 1957 beating Tabasco Road starring Speedy Gonzales and his drunk friends; both shorts were eventually given Blue Ribbon reissues. When Eddie Selzer died, the statuette was passed on to Mel Blanc, who said that this was his favorite cartoon to do voices for, especially when it came to Sylvester.