In 1987, Palmer talked with McLaren boss Ron Dennis about becoming the team's No. 2 driver to double World Champion Alain Prost. Dennis ultimately signed Stefan Johansson, and Palmer joined Tyrrell a week before the season's opening race in Brazil. Although outpaced by its turbocharged competitors, Tyrrell's naturally-aspirated Cosworth-powered car proved reliable, and it was nimble on tighter circuits. Palmer won championship points in three races, and it was in the Australian Grand Prix that he achieved his career-best fourth-place finish. He also won the Jim Clark Cup, a championship for drivers of normally aspirated cars. He stayed with Tyrrell for the next two seasons, during which his best results were two 5th-place finishes and three 6th. At the end of 1989 he signed as McLaren's test driver.