Integrated magnitude substitutes the r.m.s. average amplitude over a pre-selected interval for the peak amplitude in the conventional body-wave magnitude formula. Frequency-band magnitude uses an equivalent quantity in the frequency domain. Integrated magnitude exhibits less scatter than conventional body-wave magnitude for short-period seismograms. Frequency-band magnitude exhibits less scatter than body-wave magnitude or integrated magnitude for both long- and short-period seismograms. The scatter of frequency-band magnitude is probably due to real azimuthal effects, crustal-transfer-function variations, errors in compensation for seismograph response, microseismic moise and uncertainties in the compensation for attenuation with distance. To observe azimuthal variations clearly, the crustal-transfer functions and seismograph response need to be known more precisely than was the case in this experiment, because these two sources of scatter can be large enough to explain all of the observed variations.