The roots lie in the spread cull and an Edward Victor control in his “Card in the Aces” from Willane's Methods for Miracles, No. 8, 1945, p. 11. Both Larry Jennings and Ed Marlo lay claim to a variant of the Victor sleight, the most popular version of which makes use of a double card, and the selection is switched for an outjogged counterfeit, while the genuine selection is culled to the bottom.
Jennings claimed to have submitted this technique to Alton Sharpe for Expert Card Mysteries, 1969, and that Sharpe didn't include it in the book.
Marlo published his Convincing Control in Hierophant, No. 3, Mar. 1970, p. 133 of the 1976 Tannen reprint, p. 16 of re-edited 1998 book version, The Legendary Hierophant. Marlo cites only his Prayer Cull and Moveable Card Pass as precursors and gives June 15, 1966, as the date he recorded the sleight in personal notes. Allan Ackerman, Harvey Rosenthal and Frank Simon followed with variant handlings.
For a time, the Jennings-Marlo debate was quite heated. In certain camps it is still a contentious topic, and is never likely to be satisfactorily resolved, since the arguments depend largely on conflicting recollections of what happened between Jennings, Marlo and Sharpe. Among the most important analyses and arguments in this debate, see:
For Jennings's side: Mike Maxwell's The Classic Magic of Larry Jennings, 1986, p. 19. Then see Richard Kaufman's Jennings '67, 1997, p. 44. Jennings claimed that Sharpe described his handling to Marlo, who then published it as his own.
For Marlo's side: In response to this accusation, Marlo claimed that Sharpe had shown him, but had not explained, a face-up sequence by Jennings that did not resemble the face-down substitution and cull that has become known as the Convincing Control, and that Sharpe confirmed this recollection of their exchange; see the foreword in Marlo's Magazine, Vol. 6, 1988, n.p. Also see Jon Racherbaumer's “Putting a Placement in Its Place,” Facsimile, No. 4, 1996, p. 13. He gives a similar summary in The Linking Ring, Vol. 86 No. 8, Aug. 2006, p. 91. And finally, see Bruce Cervon's unpublished commentary, circulated by e-mail, that closely followed the publication of Jennings '67.