A giver rapier head (1) comprises a presentation space (9) between a successive guide nose (11), for leading off warp threads (23) on one side (7), and a selection nose (8), for leading off warp threads (23) on the other side, so that a weft thread (2) can be directly presented in this presentation space (9) and can engage from there in an insertion space (15) between the selection nose (8) and the first-mentioned side (7). A giver rapier (1) has a limit guide arc (10) which is arranged at the front side of the giver rapier (1) and a selection nose (8) which is arranged on the top side, with its top (26) facing the guide arc (10). A rapier weaving machine (20) comprises such a giver rapier head (1). In a method for inserting a weft thread (2), the giver rapier head (1) is moved towards this weft thread (2) while the reed (19) beats up an inserted weft thread (2).