We call a planar iterated function system box-like with rotations if the defining maps have diagonal or anti-diagonal linear parts with both types present. Up to a linear change of coordinates, IFSs of this type are exactly the irreducible but not strongly irreducible systems, the last open case between the strongly irreducible systems settled by B\'ar\'any--Hochman--Rapaport and the reducible systems of the self-affine carpet literature.
Under a projective exponential separation condition, we show that the Hausdorff dimension of the attractor equals its affinity dimension whenever the affinity dimension is at most 2− \lambda_1/\lambda_2, where \lambda_2 < \lambda_1 < 0 are the Lyapunov exponents of the equilibrium state. The talk is based on a joint work with Demi Allen, Antti K\"aenm\"aki, K\'aroly Simon, and Sascha Troscheit.