LittleMango, the best inside source I've seen is from The Last Testament of Lucky Luciano. I believe Lucky's version as it involved his family and he was close to Albert.

Albert was in hot water over the murder of Morris Diamond- he was an uncooperative union official, who threatened to go to Tom Dewey. Albert was at the top of Murder, Inc, and gave the order. One of the hitmen, Allie "Tick Tock" Tannenbaum had flipped and had implicated Albert.

Bugsy whacked mobster Harry Greenberg in Los Angeles, because he was considered a threat to flip. At the time, there was a manhunt for Bugsy, as he was in hiding. Reles was a corroborating witness for both murders....so he had to go.

Frank Costello was the acting boss of the Luciano (Genovese) family at the time and went to see Lucky at Dannemora prison. He was seeking approval to whack Reles after explaining to Charlie that it would cost plenty of money. Charlie approved it, but requested that Bugsy come out of hiding and give himself up after all of the details were planned, but before the hit.

Reles was under constant surveillance and Costello needed the cops to commit the murder. The crooked cop in charge was named Frank Bals. He arranged everything and it cost around $50,000, which he distributed. At the time, he was in the room, supervising the events. They hit Reles on the head with a billy club while he was sleeping, and then tossed him out the window. Without Reles as the corroborating witness, the charges/investigations were dropped against both Bugsy and Albert.

Bill O'Dwyer, who was also on the take, conveniently appointed Bals to handle the investigation of Reles' death. Within hours, Bals concluded that no foul play was involved. He came up with several silly theories, such as Reles trying to escape, playing a practical joke, or committing suicide.

Later, when Bill O'Dwyer was the mayor of NYC, he appointed Bals to Deputy Police Commissioner. And Bals was the bagman for the mob, bringing in $10,000 weekly and distributing the cash as he saw fit.