Scatterplots are the method of choice for displaying the distribution of points in two
dimensions. They are used to discover patterns such as holes, outliers, modes, and
association between the two variables. A common problem is overstriking, the overlap on
the plotting surface of glyphs representing individual observations. Overstriking can
create a misleading impression of the data distribution. The variable resolution bivariate
plots ({\em Varebi plots}) proposed in this paper deal with the problem of overstriking by
mixing display of a density estimate and display of individual observations. The idea is
to determine the display format by analyzing the actual amount of overstriking on the
screen. Thus, the display format will depend on the sample size, the distribution of the
observations, the size and shape of individual icons, and the size of the window. It may
change automatically when the window is resized. Varebi plots reveal detail wherever
possible, and show the overall trend when displaying detail is not feasible.