Hoylandswaine could be set for a quarter-final clash with Kirkburton in the Heavy Woollen Cup after beating fellow Drakes League Premiership side Shepley.
Only a 20-over match was possible at Marsh Lane because of rain, with Shepley restricted to 128-9 thanks to Swaine skipper Richard Wilkinson picking up three for 29.
Dan Wood with 47 and skipper Danny Glover with 28 were the best of the home batsmen.
Alex Morris again led the Swaine chase with a fine 61 and, with SP Singh hitting 38, they recorded a six-wicket win. Shahzada Khan picked up three for 28 for Shepley.
Barkisland, meanwhile, lost by 28 runs to Woodlands in a 30-over second-round tie.
Sam Frankland with 73 and Jordan Laban on 36 not out took Woodlands to 236-6 despite a three for 30 return from Ben Westbrook.
Luke Bridges led the Barkisland reply with 62, while Seth Oddy pitched in with 34, but they were held short on 208 all out as Sarfraz Ahmed took three for 30.
Three more second-round ties involving Drakes League clubs are due to be played this coming Sunday, June 7.
Skelmanthorpe visit New Farnley for the chance to travel to Townville in the last eight, Kirkburton go to Methley with the prize of a game at Hoylandswaine in round three, and Delph travel to Gomersal, with the winners at home to Hanging Heaton or Pudsey Congs, who also play this coming Sunday.
Quarter-final draw: Townville v New Farnley or Skelmanthorpe, Woodlands v Wakefield Thornes, Gomersal or Delph v Hanging Heaton or Pudsey Congs, Hoylandswaine v Methley or Kirkburton.
