The method for weaving low flaw cloths (4) comprises an elimination of weft thread sections which have irregularities (22, 22). The method is carried out by means of a weaving machine (1) which in the presence of an irregularity on a weft thread (2) to be woven can be controlled in such a manner that at least one weft thread section which comprises the irregularity can be removed from the cloth being formed after an insertion operation. The irregularity is in each case detected by a sensor (23a, 23b, 23c) prior to the feeding in of the weft thread into a thread store (21). After the detection of the irregularity an incorporation of the weft thread into the cloth is prevented in that a shed forming apparatus (100), for example a dobby for the moving of heald frames (10), is controlled in such a manner that that all warp threads (3) of the cloth to be formed are deflected either downwardly or upwardly into positions to the side of a weft thread insertion line (2). After the insertion operation the non-incorporated weft thread section is removed; or the weft thread sections are removed after two or more insertion operations.