The technique of determining the position of individual fluorescent molecules with nanometer resolution, called FIONA, has become an important tool for several biophysical applications such as studying motility mechanisms of motor proteins. The position determination is usually done by fitting a 2-D Gaussian (x-y vs. photon number) to the emission intensity distribution of the fluorescent molecule. However, the intensity distribution of an emitting molecule depends not only on its position in space, but also on its three-dimensional orientation. Here, we present an extensive numeri-cal study of the achievable accuracy of position determination as a function of molecule orientation. We compare objectives with different numerical apertures and show that an effective pixel size of 100 nm or less per CCD pixel is required to obtain good positional accuracy. Nonetheless, orienta-tion effects can still cause position errors for large anisotropy, as high as 10 nm for high numerical aperture objectives. However, position accuracy is significantly better (< 2.5 nm) when using objectives with a numerical aper-ture of 1.2. Of course, probes with lower anisotropy decrease the positional uncertainty.