Dempster first toured with New Zealand in 1927, when no Test matches were played, and headed the touring team's first-class batting averages. He was a surprise choice for the tour, being selected more for his performances in second-class cricket. In the 1929–30 MCC tour of New Zealand Dempster and Mills put on a New Zealand record first-innings stand of 276 for the first wicket, which remained the highest for New Zealand until 1972 [https://web.archive.org/web/20080804014943/http://howstat.com/cricket/Statistics/Matches/MatchOpeningStands200.asp?SortOrder=Stand]. In the 1931 New Zealand tour of England he averaged 59.26 and scored 120 in the Test at Lord's. In 1932 he was listed as one of the Wisden Cricketers of the Year.