The invention relates to a method and a device for producing fine multifilament threads from a polymer melt. A plurality of filaments are extruded, cooled, and combined in bundles so as to form a respective thread. The threads are drawn by multiple godets and wound into multiple coils. The aim of the invention is to guide the threads in a stable manner even with very fine thread titers. According to the invention, this is achieved in that the threads are combined into multiple thread bundles before being drawn. The thread bundles are guided and drawn parallel to one another on the godets and separated again into individual threads after being drawn. For this purpose, a thread bundle guide is provided on an outlet side of a drawing device.