During weft yarn insertion in a loom, as the end of weft yarn insertion approaches, a controllable yarn deviation brake (B), positioned between a weft feeder (M) and a warp shed (F) of a loom (D) brakes the weft yarn (Y) with a high braking force, causing a deviation of the yarn deviation brake which subsequently smooths down a tension peak of the yarn, so as to partially reduce the yarn brake deviation back towards the starting position, or position having no deviation. The same function is performed upon cutting of the weft yarn (Y). After braking and reduction of the yarn tension peak, during the weft insertion step, the braking force is reduced to a level correlated to the yarn tension which prevails up to cutting of the weft yarn (Y).