As a leader, Byard recorded a string of albums for the Prestige label during the 1960s. Some of these albums included Richard Davis on bass and Alan Dawson on drums, a trio combination described by critic Gary Giddins as "the most commanding rhythm section of the '60s, excepting the Hancock-Carter-Williams trio in Miles Davis's band", although it existed only for recordings. One such album was "Jaki Byard with Strings!", a sextet recording that featured Byard's composing and arranging: on "Cat's Cradle Conference Rag", each of five musicians "play five standards based on similar harmonies simultaneously". A further example of Byard's sometimes unusual approach to composition is the title track from "Out Front!", which he created by thinking of fellow pianist Herbie Nichols' touch at the keyboard. Popularity with jazz critics did not translate into wider success: a "Washington Post" review of his final Prestige album, "Solo Piano" from 1969, remarked that it was by "a man who has been largely ignored outside the inner circles". Giddins also commented in the 1970s on the lack of attention that Byard had received, and stated that the pianist's recordings from 1960 to 1972 "are dazzling in scope, and for his ability to make the most of limited situations". Following his time with Prestige, Byard had more solo performances, in part because of his affection for musical partners he had become close to but who had then died.