We report neutron diffraction measurements of the magnetic structures in two pyrochlore iridates, Yb₂Ir₂O₇ and Lu₂Ir₂O₇. Both samples exhibit the all-in-all-out magnetic structure on the Ir⁴⁺ sites below T_N ≃ 150 K, with a low temperature moment of around 0.45 μ_B/Ir. Below 2 K, the Yb moments in Yb₂Ir₂O₇ begin to order ferromagnetically. However, even at 40 mK the ordered moment is only 0.57(2) μ_B/Yb, well below the saturated moment of the ground state doublet of Yb³⁺ (1.9μB/Yb), deduced from magnetization measurements and from a refined model of the crystal field environment, and also significantly smaller than the ordered moment of Yb in Yb₂Ir₂O₇ (0.9 μ_B/Yb). A mean-field analysis shows that the reduced moment on Yb is a consequence of enhanced phase competition caused by coupling to the all-in-all-out magnetic order on the Ir sublattice.