A fiber application head comprising a compaction system including a plurality of independent compaction rollers and compaction cylinders and, for each fiber, cutting means and rerouting means. For each fiber, the head comprises a functional module including the cutting means and the rerouting means, each functional module is mounted so as to be movable in translation on a support element of the head. Each compaction roller is mounted on one or more adjacent functional modules. A compaction cylinder is associated with the functional module(s) associated with a compaction roller for the displacement in translation of the functional module(s). An independent heating system is associated with each compaction roller, and able to displace with the functional module(s) associated with a compaction roller.