A revised version of the storm-time disturbance index D_st 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 D_st. 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 D_st^5807-4SH. Comparisons are made with the standard Kyoto D _st. Various biases, especially for residual solar-quiet variation, are identified in the Kyoto D_st, and occasional storm-time errors in the Kyoto D_st are noted. Using D_st^5807-4SH, 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 D_st^5807-4SH is useful for a variety of space physics and solid-Earth applications, it is made freely available to the scientific community.