In Roger Clemens' four highest strikeout games, he didn't walk a batter. (Note: He also struck out 16 twice during 1988 season, both times against Kansas City, but walks not available):

Date .. K's .. BB .. Opp. .. Won

9/18/96 20 .... 0 .. Det. .. 4-0

20 .... 0 .. Sea. .. 3-1

18 .... 0 .. K.C. .. 3-0

16 .... 0 .. Bos. .. 3-1