We have studied SUMER and CDS time series of spectra and images of quiet-Sun regions at the solar disc centre. The data contain ultraviolet emission lines sampling temperatures of the chromosphere, transition region and corona. We find a high correlation between average net Doppler shifts and relative brightness variabilities of the studied lines (correlation coefficient of 0.92), suggesting a connection between the two quantities. The anti-correlation between differential emission measures and relative brightness variabilities is weaker (correlation coefficient of -0.78). We discuss the observed relationships on the basis of differential emission measures and linear wave calculations.