We study the consequences of recently proposed recursions [1] for the anisotropic spin‐1/2 Heisenberg model, based on a generalization of the Migdal approximation [2]. In the isotropic case [3], they give the correct lower critical dimension, 2, and yield &ngr;=1/&egr; in (2+&egr;) dimensions as &egr;→0. In three dimensions, &ngr;=1.40 and &fgr;=1.56. The recursions give a finite entropy and linear specific heat as T→0. They give a reasonable description of Ising‐like anisotropy, but a strange and qualitatively incorrect picture of the XY side: first, there is no XY fixed point (fp) at T=0, and in three dimensions a flow from the finite‐T XY fp leads to the T=0 Heisenberg fp. Second, there is a jump (as opposed to flow) behaviour in the first iteration of any point in a large region of the anisotropy‐temperature plane. Third, the finite‐T fp persists in fewer than 2 dimensions, and a new finite‐T XY fp also appears; both are spurious. We also study the sensitivity of the results on b, and find that unlike the Migdal approximation for classical systems, here even the lower critical dimension in the isotropic case depends on b.