A twisted helically-shaped member (15) in the form of a twisted tie, twisted fastener, twisted wire or twisted rod; said twisted helically-shaped member (15) having an axial core (12) and a plurality of helical threads (13H) extending along the axial core (12); and wherein a variation in lead measurements along the length of at least one helical thread (13H), is less than a variation in pitch measurements along the lengths of the helical threads (13H); wherein the axial core (12) has a transverse cross-sectional area comprising two-fifths or less of the transverse circumscribed cross-sectional area of the helical threads (13H).