A controlled weft thread presenting and clamping arrangement minimizes weft thread waste and ensures proper tensioning of the weft thread during its presentation to the insertion gripper, in a gripper loom for weaving with plural different weft threads. The arrangement includes a control shaft (13) that has a drive key (14) protruding therefrom in a reference plane (7), and that is rotatably supported on a support bracket (10, 11, 12), which may be mounted on the loom. Weft thread presenting levers (15) each carrying a respective clamp (16) are movably arranged on the shaft (13), which passes through a hole in each of the presenting levers (15). A translational drive (22) acts on a presenting lever support (17) to translationally move all of the presenting levers (15) in unison together axially along the shaft (13) until a selected lever (15) is positioned in the reference plane (7), with the lever's drive groove 15B engaged on the drive key (14) of the shaft (13). A rotational drive (23) rotates the shaft (13), and therewith the selected thread presenting lever (15) via the drive key (14). A guide member (19) has a lengthwise groove (20) to allow all of the presenting levers (15) to move linearly therealong in unison, and a crosswise groove (21) in the reference plane (7) to allow only the selected presenting lever (15) to rotate in the reference plane. A thread back tensioning device (9) is arranged in the thread path to apply tension to the thread being presented to the gripper.