We provide a new characterisation of Duquesne and Le Gall's α-stable tree, α ∈ (1, 2], as the solution of a recursive distribution equation (RDE) of the formwhere g is a concatenation operator, ξ = (ξ i , i ≥ 0) a sequence of scaling factors, T i , i ≥ 0, and T are i.i.d. trees independent of ξ. This generalises a version of the well-known characterisation of the Brownian Continuum Random Tree due to Aldous, Albenque and Goldschmidt. By relating to previous results on a rather different class of RDE, we explore the present RDE and obtain for a large class of similar RDEs that the fixpoint is unique (up to multiplication by a constant) and attractive.