NORESS recordings of nuclear explosions in central Asia (Δ = 38°) provide new spectral attenuation estimates for frequencies from about 3 to 15 Hz. Two path spectra, representing propagation losses from the Shagan River and Degelen test sites to southern Norway, are calculated using the double-averaging technique of Bache et al. (1985, 1986). Both paths exhibit less attenuation than previously documented for explosions recorded teleseismically at the UKAEA arrays over the 1- to 8-Hz frequency range. The Shagan and Degelen spectra have somewhat different decay rates, perhaps reflecting variations in average source properties. Since the NORESS data extend to higher frequencies than previously available for attenuation measurements, we compare the NORESS spectral data to published models derived from NORSAR data (1 to 8 Hz) for the same path. The Degelen-NORSAR model is compatible with the NORESS data to about 7 Hz, but from 7 to 15 Hz, it predicts higher spectral amplitudes than are observed Using a hybrid absorption band-constant t* formulation, new models are derived which fit both the Shagan River path spectrum (t0* = 0.6 sec, τm = 0.05 sec, (t1* = 0.07 sec) and the Degelen spectrum (t0* = 0.6 sec, τm = 0.05 sec, (t1* = 0.05 sec) from 3 to 15 Hz. The NORESS data support frequency-dependent t* in the 3- to 15-Hz frequency range. The results also demonstrate that extrapolation of attenuation models obtained from longer period data to shorter periods may not predict the correct spectral levels. Actual high-frequency measurements are needed in order to characterize attenuation behavior at high frequencies.