Abstract The fcc slip-systems hardening inequalities given in [Havner, K.S., 2005. On lattice and material-frame rotations and crystal hardening in high-symmetry axial loading. Philos. Mag. 85 (25), 2861–2894] are investigated in (1 1 0) channel die compression for the 35.26° range of lateral constraint directions from ( 1 1 ¯ 1 ¯ ) (the ‘brass’ orientation) to ( 1 1 ¯ 0 ) (the ‘Goss’ orientation). It is established analytically that the inequalities uniquely predict lattice stability and finite shearing about the (1 1 0) load axis, consistent with experiments in this range. An analysis of the continuation of lattice stability to large deformations leads to a critical strain at which the lattice could theoretically, but not necessarily, lose stability.