"Compressed Hare" is the 4th & final pairing of Bugs Bunny and Wile E. Coyote, and, aside from a Road Runner featurette a year later, it would be the last time that Wile would talk.
I'm thinking that Chuck Jones was looking for a new nemesis for Bugs, considering that they were running out of plot ideas for Bugs with either Elmer Fudd or Yosemite Sam. "Compressed Hare" is also the last of the Coyote "Super Genius" trilogy. The only other Bugs-Wile pairing saw Bugs sub for the Road Runner.
Bear with the video, as some tweaks were made to avoid the WB copyright patrol.
Wile's business card should've had him described as a "professional glutton for punishment", don't you think?