Simple spectral ratio (ssr) and horizontal-to-vertical (h/v) site- response estimates at 47 sites in the Puget Lowland of Washington State document significant attenuation of 1.5- to 20-Hz shear waves within sedimentary basins there. Amplitudes of the horizontal components of shear-wave arrivals from three local earthquakes were used to compute ssrs with respect to the average of two bedrock sites and h/v spectral ratios with respect to the vertical component of the shear-wave arrivals at each site. ssr site-response curves at thick basin sites show peak amplifications of 2 to 6 at frequencies of 3 to 6 Hz, and decreasing spectral amplification with increasing frequency above 6 Hz. ssrs at nonbasin sites show a variety of shapes and larger resonance peaks. We attribute the spectral decay at frequencies above the amplification peak at basin sites to attenuation within the basin strata. Computing the frequency-independent, depth-dependent attenuation factor (Qs,int) from the ssr spectral decay between 2 and 20 Hz gives values of 5 to 40 for shallow sedimentary deposits and about 250 for the deepest sedimentary strata (7 km depth). h/v site responses show less spectral decay than the ssr responses but contain many of the same resonance peaks. We hypothesize that the h/v method yields a flatter response across the frequency spectrum than ssrs because the h/v reference signal (vertical component of the shear-wave arrivals) has undergone a degree of attenuation similar to the horizontal component recordings. Correcting the ssr site responses for attenuation within the basins by removing the spectral decay improves agreement between ssr and h/v estimates.