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Gravesend closed to within three points of London 2 South leaders Cobham with Saturday's 28-6 home win over Tunbridge Wells.
The visitors started strongly and Ollie Rogers kicked a drop goal to put them 3-0 ahead.
Gravesend responded through Gary Gray who kicked three long-range penalties to give his side a 9-6 lead.
Gravesend continued to pressurise Tunbridge Wells in the second half but Rogers' range from penalties was poor as he missed four in three minutes.
After that escape, Gravesend turned the screw as they found a way through the Tunbridge Wells defensive line.
Matt Weighman was the first to touch down, followed by Adam Bishop and Terry Papworth. Gray converted twice to put a gloss on Gravesend's performance.