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Removing extraneous points near the centre of a QQ-plot

I'm trying to plot a QQ-plot with two data sets of about 1.2 million points, in R (using qqplot, and feeding the data into ggplot2). The calculation is easy enough, but the resulting graph is painfully slow to load, because there's so many points. I've tried linear approximation to reduce the number of points to 10000 (this is what the qqplot function does anyway, if one of your data sets is bigger than the other), but then you lose a lot of the detail in the tails.

Most of the data points towards the centre are basically useless - they overlap so much that there's probably about 100 per pixel. Is there any simple way of removing data that is too close together, without loosing the more sparse data toward the tails?