After driving his own car during a handful of races in the 1993 season's first half, Speed was called to drive for Robert Yates Racing, filling in following Davey Allison's death. Speed qualified fourth at Watkins Glen International. He followed that up with a second place start at Michigan and a seventh-place finish. The next race at Bristol, Speed was running a strong race before contact late with Rick Mast ruined his chances at a top ten finish. After Bristol, Speed was replaced by Ernie Irvan, but less than a week later, on September 3, it was announced that Speed would drive the #15 Ford owned by Bud Moore for 1994, replacing Geoff Bodine, who would depart from Moore's Ford to drive his own team which he purchased following Alan Kulwicki's death. However, two races later at Dover, Speed replaced Bodine in Moore's #15, as Ford allowed Bodine to take over Kulwicki's former #7 for the last seven races of 1993, in preparation for his first full season as an owner-driver. Speed's best finish for Moore at the end of the '93 season was an eleventh at Charlotte.