In 1978, Means began running as an independent driver, except for the Winston 500, where he drove for Bill Champion. He had two top-tens and improved three spots to finish sixteenth in points. He received new sponsorship from Mr. Transmission, but only had one top-ten in 1979, forcing him to fall to 23rd in points. After a sponsorship change to Thompson Industries for 1980, Means failed to finish higher than 12th, but he was still able to move up to 17th in the standings. Broadway Motors became his new sponsor in 1981, and after two top-tens, he continued to move up to fourteenth in points. In 1982, he was able to garner an additional pair of ninth-place runs, and finished a career-best 11th in points. It also marked the first time in his career he ran every race on the schedule.