SOLUTION TO PUZZLE No. 8585:

ACROSS: 3 Lay brother; 8 Demure; 9 Gain; 10 West Indies; 11 Dim; 13 Pier; 14 Leaking; 15 Dray; 17 Shark; 20 Pages; 22 Weed; 24 Cajoles; 25 Rita; 27 Nod; 28 Sea-serpent; 29 Gale; 30 Tarmac; 31 Dispatches.

DOWN: 1 Meredith; 2 Butter; 3 Leonard; 4 Yogis; 5 Rags; 6 Handling; 7 Rummages; 12 Warp; 14 Lyre; 16 Rows; 17 Seconded; 18 Adjudges; 19 Kilo; 21 Estonian; 23 Directs; 25 Report; 26 Watch; 28 Seat.