This knowledge started a quest to find out more about Joe Dodge. The most detailed resource is Joe Dodge: The Drummer as Time-Keeper from Steven Cerra's excellent blog, Jazz Profiles. As a side note, almost every time I need information about relatively obscure musicians I invariably find it in Mr. Cerra's blog.
While reading Cerra's account of Dodge, it became apparent why Paul Desmond was so incensed when Brubeck hired Morello. That story is well told in When drummer Joe Morello joined the Dave Brubeck Quartet, which was excerpted from Paul Ramsey's Take Five: The Public and Private Lives of Paul Desmond.
Here are a few clips of Dodge in action with the Dave Brubeck Quarter circa 1956:
Dodge is straight ahead and low key, which is a direct contrast to Morello's playing. I love them both, but for different reasons. Morello certainly raised the bar in jazz drumming, but Dodge's restrained drumming complemented Paul Desmond's playing better - and I have always held that Desmond was the heart and soul of the Quartet.
It's probably not a little surprising that after Desmond struck out on his own that he chose Connie Kay for the drum chair. Kay's tasteful and restrained drumming was similar to Dodge's approach, and complemented Desmond's saxophone in ways that Morello's playing didn't.
Lest you get the impression that I am criticizing Morello, know that I consider him to be among the top ten drummers in history, and thoroughly enjoy his playing. Here is Take the A Train with Morello in the drum chair - contrast it with the way Dodge played it in the clip after it to see the differences in their approaches. Both renditions are excellent, and both are valid. My preference is Dodge's playing:
If you want to hear more Joe Dodge and the early incarnation of the Dave Brubeck Quartet, I recommend Jazz: Red, Hot and Cool, as well as Jazz Goes to College. These two albums have live tracks that showcase Dodge's drumming style and how it supported Desmond.