A multi-material two-phase hybrid model of heterogeneous explosives, with a reaction rate that is proportional to the gas-phase pressure excess above an ignition threshold, is examined computationally. The explosive is confined within a compliant inert, and the focus is on the behavior of an established detonation as it rounds a 90° corner and undergoes diffraction. The numerical approach, a variant of Godunovʼs method, is designed to capture interfaces between materials that can undergo phase change, and extends previous work of the authors on rigidly-confined two-phase detonations. The dependence of the post-diffraction conduct on the strength of the confinement is explored by holding the reaction-rate prefactor and the ignition threshold fixed, and considering confiners of two different strengths. The aim is to determine whether a detonation that turns the corner successfully when rigidly confined can experience failure when the confinement is compliant.