A more plausible answer.
Another version, now part of popular lore, was that for several months Dorsey refused the $60,000 that Jules Stein had offered him to release Sinatra from his contract, simply because Dorsey had grown to despise Sinatra and intended to hold on to his contract and drive the singer's career into the ground, which he could easily do by simply keeping him off stage and radio.
But, Sinatra's strong willed and politically connected mother went to see New Jersey's Mafia boss, Quarico Moretti, better known as Willie Moretti, who controlled large parts of the East Coast entertainment industry. In fact, by the early 1940s, the national syndicate still held a virtual lock on the entertainment business unions nationwide and Mobsters were always looking to expand their control of the industry by managing the careers of promising entertainers.
Moretti saw that Sinatra's prospects were good, and agreed to get the young man released from his contract with Dorsey for a cash payment from Sinatra, plus a percentage of his future earnings. Working through Jules Stein, Moretti's first offer to Dorsey was $60,000 cash. When Dorsey turned that down, Moretti, who was considered, in mob circles, to be a madman, decided to take matters into his own hands, and make the band leader an offer he couldn't refuse.
One night after a show, Moretti pushed his way into Dorsey's dressing room, put a gun in the band leader's mouth and told Dorsey to sell Sinatra's contract. Which he did. For one dollar.
As for the $60,000 paid by MCA to release Sinatra, supposedly that money, in cash, went directly from Dorsey's bank account into Moretti's greedy little hands, after Dorsey paid the taxes on it.
Sinatra always denied the story too, and claimed he barely knew Moretti, who lived only a few doors away from him in suburban New Jersey.
Dorsey spent the rest of his life denying the gun in the mouth story, but in 1951, right after Moretti was killed, Dorsey only added credence to the tale, when he told American Mercury Magazine that he signed the contract releasing Sinatra because one night, three men paid him in his dressing room, placed Sinatra's release in front of him and said, "Sign it or else!"http://www.americanmafia.com/Feature_Articles_212.html