Estimates of the spectral linewidths of low degree (Q=0 and Q=1) 5 min p-modes obtained from Doppler shift observations in 1984, 1986, and 1987 are reported. The observed linewidths increase from 0.5 microHz at 2000 microHz to 3.8 microHz at 4300 microHz for Q = 0. Comparison with other data suggests that for a given frequency the linewidth increases with increasing Q value. On the assumption that the linewidth is substantially due to damping processes the line widths are consistent with e-folding times between 3.7 and 0.5 days.