Auditory-nerve spike trains exhibit fractal behavior, and therefore traditional renewal-point-process models fail to describe them adequately. Previous measures of the fractal exponent of these spike trains are based on the Fano factor and consequently cannot exceed unity. Two estimates of the fractal exponent are considered which do not suffer from this limit: one derived from the Allan variance, which was developed by the authors, and one based on the periodogram. These measures indicate that fractal exponents do indeed exceed unity for some nerve-spike recordings from stimulated primary afferent cat auditory-nerve fibers.