PALMERSTON booked their ticket into the third round of the Canada Life Denny Plate with a 79-68 win against Bournemouth.
Livi Bell and Tony Grant were the Fareham club's match-winners setting up a date on Saturday, November 18, with Worthing, who were 87-64 winners against Isle of Wight.
Bell defeated Clive Bunford 28-14 with Grant outpointing Paul Turner 25-15.
Palmerston lost the other two contests. Neil Donovan fell 22-14 to Chris Daniels, and Barry Grinaway finished 17-12 down to Colin Garment.
Rushmoor ousted Jack Hi 86-65 and now face a formidable test in Cambridge Park from Twickenham.
Isle of Wight Community, who had a walk-over against Isle of Purbeck (Swanage), play Victory who swamped Dolphin 92-60 helped by the runaway 31-8 triumph of Steve Robertson's rink over Bob Atkins at Poole.
Atherley's England international Peter Ward, who reached the quarter-finals of the national singles last winter, coasted through to the third round of this season's competition.He ran out a 21-10 winner against Jon Plomer (East Dorset).
Barry Bendall (Banister Park) eclipsed Ron Stoneham (Atherley) 21-10 but Bendall's club colleague Mike Slade was squeezed out 21-20 by Dave Durrant (Atherley).
Dave Archibald lost 21-15 to former England indoor singles king Andy Ross (Longmeadow) and the Atherley man also bowed to club colleague Peter Rathband by the same score in the over-60s' singles.
In an all-Banister Park seniors' tussle, Ken Marsh outgunned Danny McEwan 21-15, while Clive Tancock (Atherley) emphatically ousted Freddie Johnson (Bourne-mouth) 21-10.
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