Recent studies have shown the ubiquity of pleiotropy for variants affecting human complex traits. These studies also show that rare variants tend to be less pleiotropic than common ones, suggesting that purifying natural selection acts against highly pleiotropic variants of large effect. Here we investigate the mean frequency, effect size and recombination rate associated with pleiotropic variants, and focus particularly on whether highly pleiotropic variants are enriched in regions with putative strong background selection. We evaluate variants for 41 human traits using data from the NHGRI-EBI GWAS Catalog, as well as data from other three studies. Our results show that variants involving a higher degree of pleiotropy tend to be more common, have larger mean effect sizes, and contribute more to heritability than variants with a lower degree of pleiotropy. Using data from four different studies, we show that more pleiotropic variants are enriched in genome regions with stronger background selection than less pleiotropic variants. Thus, we conclude that even though highly pleiotropic variants found so far have larger average effect sizes and frequencies than less pleiotropic ones, they are likely to be subjected to stronger background selection.