The title of the short is an pun on the term "sweet dreams".
At the Dog and Cat Clinic, psychiatrist Dr. Milt Towne sees Sylvester, who is having a nervous breakdown. He recounts a short scene from his boyhood where his father wouldn't teach him how to catch mice (actually a scene of Sylvester Junior from "Too Hop To Handle", though using the establishing shot from the opening of "Cheese it, the Cat!"). Then he tells of his troubles trying to fish and first meeting Tweety (in flashbacks from "Sandy Claws").
Sylvester then tells the doctor about trying to catch Tweety at the circus (as seen in "Tweety's Circus"). Then about his embarrassment when he hid in Granny's knitting basket and his fur was knitted into a sweater (as seen in "A Street Cat Named Sylvester"). Finally, he relates the tale of Tweety shooting him in the face with a gun and Granny shooting him in the face with a plunger (scenes from "Gift Wrapped").
Sylvester notices that the doctor is snoring. When he wakes up, the doctor makes an excuse about having to fly to Detroit for an appointment that afternoon, and he jumps out the window and literally flies away. Sylvester flies out the window after him.
ABC's The Bugs Bunny & Tweety Show cut the scene from "Tweety's Circus" where the elephant hits Sylvester with his trunk, as well as the Hopalong Cassidy/Indian sequence from "Gift Wrapped" as it is when said short aired on the show (Cartoon Network and Boomerang however have aired this short uncut despite airing "Gift Wrapped" in edited format). It should be noted that the elephant scene was left alone when "Tweety's Circus" aired on ABC. 
- It is the only appearance of Sylvester Junior and Tweety in the same cartoon, though the two never interact, and the footage of Junior is said to be a flashback of a young Sylvester.
- The Apartment Building used in the first flashback was borrowed from "Cheese It, the Cat!"
- Most of this cartoon was used in the Thanksgiving special, Bugs Bunny's Thanksgiving Diet.
- Granny and Tweety's respective screen times in this cartoon are limited to flashbacks (in the form of archive footage).
- Although all the other Cartoon Network and Boomerang stations (including the USA) air horribly faded copies of the cartoon, a remastered (but unrestored) copy of the cartoon has been released on the Italian VHS release Silvestro e Gonzales: Matti e mattatori (as pictured in the second video in the infobox), but hasn't been released on DVD yet.
TV Title Cards
|1942||A Tale of Two Kitties|
|1944||Birdy and the Beast|
|1945||A Gruesome Twosome|
|1948||I Taw a Putty Tat|
|1949||Bad Ol' Putty Tat|
|1950||Home Tweet Home • All a Bir-r-r-d • Canary Row|
|1951||Putty Tat Trouble • Room and Bird • Tweety's S.O.S. • Tweet Tweet Tweety|
|1952||Gift Wrapped • Ain't She Tweet • A Bird in a Guilty Cage|
|1953||Snow Business • Fowl Weather • Tom Tom Tomcat • A Street Cat Named Sylvester • Catty Cornered|
|1954||Dog Pounded • Muzzle Tough • Satan's Waitin'|
|1955||Sandy Claws • Tweety's Circus • Red Riding Hoodwinked • Heir-Conditioned|
|1956||Tweet and Sour • Tree Cornered Tweety • Tugboat Granny|
|1957||Tweet Zoo • Tweety and the Beanstalk • Birds Anonymous • Greedy for Tweety|
|1958||A Pizza Tweety-Pie • A Bird in a Bonnet|
|1959||Trick or Tweet • Tweet and Lovely • Tweet Dreams|
|1960||Hyde and Go Tweet • Trip for Tat|
|1961||The Rebel Without Claws • The Last Hungry Cat|
|1962||The Jet Cage|
|1964||Hawaiian Aye Aye|
|2011||I Tawt I Taw a Puddy Tat|