In medicine a number of fiber-applications for laser power transmission are used on a routine basis. For example several watts of laser power out of an argon laser ( λ = 488 nm and 514 nm) are transmitted through fibers for ophthalmic surgery. Especially adapted fibers with core diameters of 50 μm or 80 μm are used. But this laser is not considered to be a "high power laser". High power lasers used in medicine are - the CO2-laser ( λ = 10.6 μm) for cutting and - the Nd:YAG-laser ( λ = 1060 μm and 1320 nm) mainly for coagulation. The beam powers are 20 - 180 W. Because fibers for the CO-laser are presently under development and thus are not yet ready for clinical use we will restrict our scope to Nd:YAG-lasers. The high power beam of the Nd:YAG-laser is usually guided through 600 μm silica fibers. But also thinner fibers should be possible. In our paper we would like to discuss whether thinner fibers are advantageous and what are the limits for reducing the fiber diameter. After a short recapitulation of fiber data the different aspects correlated to the fiber diameter are reviewed. Each aspect is discussed in detail and finally conclusions are given as to which fiber diameter seems most appropriate depending on the desired application.