As Internet use becomes widespread at home, parents are trying to maximize their children's online opportunities while also minimizing online risks. We surveyed parents of 6- to 14-year-olds in 8 European countries (N=6,400). A factor analysis revealed 2 parental mediation strategies. Enabling mediation is associated with increased online opportunities but also risks. This strategy incorporates safety efforts, responds to child agency, and is employed when the parent or child is relatively digitally skilled, so may not support harm. Restrictive mediation is associated with fewer online risks but at the cost of opportunities, reflecting policy advice that regards media use as primarily problematic. It is favored when parent or child digital skills are lower, potentially keeping vulnerable children safe yet undermining their digital inclusion.