A blind fastener setting device includes a drawing mechanism and an adjustably supported tip piece. The tip piece has several mandrel guide channels, each of which can be aligned with respect to the drawing mechanism. The tip piece can be easily adjusted without the overall size of the device having to be enlarged to any significant extent. The tip piece has a cross-sectional shape of a polygon which has an uneven number of sides. The mandrel guide channels each extend from a side to the oppositely disposed corner.