We prove an isoperimetric inequality for probability measures μ on R n with density proportional to exp(−φ(λ|x|)), where |x| is the euclidean norm on R n and φ is a non-decreasing convex function. It applies in particular when φ(x) = x α with α ≥ 1. Under mild assumptions on φ, the inequality is dimension-free if λ is chosen such that the covariance of μ is the identity.