The impact of missing values on the centennial-scale variability of heavy precipitation was analysed using daily data from European rain gauges. Sub-sampling was modeled according to the observed structure of gaps in daily precipitation records. Quantitative estimates of the sampling impact on the long-term variability derived from high-quality long-term station data were used for the homogenization of sampling in European time series and the estimation of long-term secular tendencies in heavy precipitation indices. Centennial linear trends of extreme precipitation based on different indices are quite robust in winter but less robust in summer, implying seasonality in the trend estimates especially in Western Europe. Estimates of annual indices derived for the locations where different indices shows significant trends imply primarily positive centennial-scale changes in heavy and very heavy precipitation with the strongest magnitudes of about 3--5% per decade in Eastern Europe.