According to the liner notes from this three disc vinyl collection I'm holding Sinatra parted ways with Harry James in late 39 and did some sessions with Tommy Dorsey. These sessions were recorded from Feb. 1940 to July 1942 and are called the The Tommy Dorsey/Frank Sinatra Sessions. I don't know if it is available on CD or the sound quality because my set is still sealed. It does say they used the Original masters for the set but on some hard to track down songs they just used copies of 78's from collectors. Hope this helps you out.
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