The resonant peaks of solar p modes show small amounts of asymmetry in frequency. Here, we use five independent sets of contemporaneous data, collected over a ~=8 yr period, to investigate whether peak asymmetry in low angular degree p modes changes over the solar activity cycle. Three of the data sets are from instruments on board the ESA/NASA SOHO spacecraft (GOLF, MDI, and VIRGO/SPM); and two are from ground-based networks (BiSON and GONG). Evidence for variation in asymmetry, well correlated with the activity cycle, is uncovered in the GOLF and BiSON Doppler velocity data. Suggestions of a similar trend are present in the GONG Doppler velocity data. Apparent changes in the MDI Doppler velocity data are somewhat less significant. Meanwhile, analysis of the SPM intensity data failed to uncover any evidence for significant change of the asymmetry parameter.