The History of McCune Trucking Byron McCune hauling 120 sack of cotton (six tons). The usual load was five tons. Hauling 3 tons of loose hay. Hauling 122 bales of hay from Casper. Byron's truck looking pretty small while hauling a house. Byron started out hauling fuel for Premium Oil. Byron and Alice. Byron in Kanab. He hauled gas from Salt Lake to Kanab. Byron and Alice, 1973. A McCune Peterbilt rig in 1985. In the early 1990s the company transitioned to dump trucks.