A method for weaving a fabric (F), with warp yarns (412, 414, 422, 424) and inwoven weft yarns (61, 62, W1-W5), on a loom (2) which comprises a warp delivery unit (8); heddles (14) for moving warp yarns in order to form a shed; a mechanism (12) for moving (F1) each heddle vertically along a vertical path; weft insertion means (21, 22) for inserting each weft yarn in a shed (S1, S2) and for releasing the weft yarn at a given location along a weft axis (Y1, Y2); and weft delivery means (28) for delivering weft yarns (61, 62, W1-W5) to the weft insertion means, this method comprising, for at least two consecutive picks, at least the following steps consisting in a) opening the shed (S1, S2); b) picking, by the weft insertion means (21, 22), of a first end (612, 622) of a weft yarn (61, 62, W1-W5) presented by the weft delivery means (28); c) drawing (A3) the weft yarn into the shed, along the weft axis (Y1, Y2); d) releasing the weft yarn at the predetermined position along the weft axis; e) withdrawing the insertion means from the shed; and f) beating-up the weft yarn wherein, during step c), the shed is closed around the inserted weft yarn (61, 62), by moving warp yarns (412, 414, 422, 424) of a predetermined group (G4, G4') of warp yarns to a semi-closed position.