A series of branched poly(ethylene terephthalate) samples was prepared by employing 0.07-0.42 mol % trimethylolpropane (TMP) for melt; polycondensation. These polymers were characterized with respect to molar mass, intrinsic viscosity, and melt viscosity. Spinning into fibers took, place at spinning speeds ranging from 2500 to 4500 m/min. The molecular orientation of the fibers as measured by birefringence and polarized fluorescence decreases with growing amounts of TMP, as does crystallinity. Thus with slightly branched polymers, higher spinning speeds than with a linear polymer can be used to achieve a certain property profile.