Sounds heard over headphones are typically perceived inside the head (internalized), unlike real sound sources which are perceived outside the head (externalized). If the acoustical waveforms from a real sound source are reproduced precisely using headphones, auditory images are appropriately externalized and localized. The filtering (relative boosting, attenuation and delaying of component frequencies) of a sound by the head and outer ear provides information about the location of a sound source by means of the differences in the frequency spectra between the ears as well as the overall spectral shape. This location-dependent filtering is explicitly described by the head-related transfer function (HRTF) from sound source to ear canal. Here we present sounds to subjects through open-canal tube-phones and investigate how accurately the HRTFs must be reproduced to achieve true three-dimensional perception of auditory signals in anechoic space. Listeners attempted to discriminate between 'real' sounds presented from a loudspeaker and 'virtual' sounds presented over tube-phones. Our results show that the HRTFs can be smoothed significantly in frequency without affecting the perceived location of a sound. Listeners cannot distinguish real from virtual sources until the HRTF has lost most of its detailed variation in frequency, at which time the perceived elevation of the image is the reported cue.