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I want to digress here and ask who the heck was Florence Rice? She's so adorable! She's really good in this. She's got a bit of a Myrna Loy thing going on (in fact, the movie is unabashedly trying to ride that Thin Man train) but she's so natural, so unaffected, so darned cute.
And Melvyn Douglas, who was always a little more goofy than dashing, actually holds his own in this one. They do a great job together and it's puzzling and disappointing that the studio did not continue the series with them.
I'm having trouble explaining the plot of Fast Company as it's not exactly linear. Basically Joel and Garda try to help a young ex-con who was convicted of stealing rare books from his fiancee's father. The girl's father is involved in his own nefarious book dealings and eventually he's bumped off and the kid is accused of murder. Garda urges Joel to take the case.
The dialog is snappy, the chemistry between the leads is strong, the plot makes as much sense as these things ever do. It's definitely entertaining.
The subsequent movies are progressively weaker although the star power is higher in the second film, Fast and Loose, with Robert Montgomery and Rosalind Russell. The third film, Fast and Furious, is painful and pretty much a complete waste of time.