Warren Commissioner John J. McCloy had serious reservations about the so-called Single Bullet Theory, according to published reports.
The magazine Newsday cites a confidential document dated June 24, 1964, as a source for the claim. That's about seven months after the assassination, and some three months before the release of the Warren Report.
The Single Bullet Theory (SBT) holds that a single bullet wounded President John F. Kennedy and Texas Governor John Connally on November 22, 1963, in Dallas, Texas.

The document, a memorandum from McCloy to the Commission's chief counsel, J. Lee Rankin, contained a critique of a draft of the Commission's final report. "I think too much effort is expended on attempting to prove that the first bullet, which hit the president, was also responsible for all of Connally's wounds," McCloy wrote. "The evidence against this is not fully stated." He added that a section of the report dealing with the possibility of shots being fired at Kennedy's motorcade from an overpass was "not well done."
McCloy also questioned the Commission's account of a bullet found on a stretcher at Parkland Hospital, where Kennedy and Connally were taken after being shot. "The statement concerning the bullet which was found on the stretcher is not particularly persuasive because there is no indication that the 'stretcher bullet' was in fact the bullet which caused the [Connally] wrist wound," he wrote.
This is the second time in as many months that revelations about the inner workings of the Warren Commission have worked against its official conclusions. The Dallas Morning News reported in July that former President and last surviving Commission member Gerald Ford edited a key sentence about a bullet that entered JFK's body. That edit to the Warren Report, critics said, resulted in wording suggesting a bullet hit Kennedy higher than it really did.
The SBT is central to the Commission's conclusion that Lee Harvey Oswald alone fired the shots that killed Kennedy and wounded Connally. The Commission declared that there was time for Oswald to fire no more than three shots and that he did, in fact, fire three times. One shot was said to have missed the presidential limousine entirely. A second --- the fatal bullet --- was said to have struck Kennedy in the back of the head. That left just one more bullet, which spawned the hotly-disputed SBT. The Commission said this bullet hit Kennedy in the lower part of the back of his neck, and went on to cause wounds to Connally's back, right wrist and left thigh.
If the Commission had concluded that separate bullets had struck Kennedy and Connally, it would have been forced to conclude there was a fourth bullet. And since there had not been time for more than three shots, it would have meant there was a second gunman.
The document was released recently by the Assassination Records Review Board, and contains many other suggestions by McCloy on revising the draft report. Some of those suggestions were adopted by the Commission. But the Commission did not revise the sections dealing with the single, or "magic," bullet theory.
According to one tally, McCloy attended just 16 of 51 Warren Commission sessions, and heard only 35 of 94 witnesses. He died in 1989.

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