A revised version of the storm-time disturbance index Dst is calculated using hourly-mean magnetic-observatory data from four standard observatories and collected over the years 1958-2007. The calculation algorithm is a revision of that established by Sugiura et al., and which is now used by the Kyoto World Data Center for routine production of Dst. The most important new development is for the removal of solar-quiet variation. This is done through time and frequency-domain band-stop filtering - selectively removing specific Fourier terms approximating stationary periodic variation driven by the Earth's rotation, the Moon's orbit, the Earth's orbit around the Sun, and their mutual coupling. The resulting non-stationary disturbance time series are weighted by observatory-site geomagnetic latitude and then averaged together across longitudes to give what we call Dst5807-4SH. Comparisons are made with the standard Kyoto D st. Various biases, especially for residual solar-quiet variation, are identified in the Kyoto Dst, and occasional storm-time errors in the Kyoto Dst are noted. Using Dst5807-4SH, storms are ranked for maximum storm-time intensity, and we show that storm-occurrence frequency follows a power-law distribution with an exponential cutoff. The epicycles of magnetic disturbance are explored: we (1) map low-latitude local-time disturbance asymmetry, (2) confirm the 27-day storm-recurrence phenomenon using autocorrelation, (3) investigate the coupled semi-annual-diurnal variation of magnetic activity and the proposed explanatory equinoctial and Russell-McPherron hypotheses, and (4) illustrate the well-known solar-cycle modulation of storm-occurrence likelihood. Since Dst5807-4SH is useful for a variety of space physics and solid-Earth applications, it is made freely available to the scientific community.