We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs-type fragmentation tree with Aldous’ beta-splitting model, which has an extended parameter range β>−2 with respect to the beta(β+1, β+1) probability distributions on which it is based. In the multifurcating case, we show that Gibbs fragmentation trees are associated with the two-parameter Poisson–Dirichlet models for exchangeable random partitions of ℕ, with an extended parameter range 0≤α≤1, θ≥−2α and α<0, θ=−mα, m∈ℕ.