Monte Carlo simulations of binary Lennard-Jones crystals with mole fraction x=0.5 are performed at constant temperature and pressure. In our symmetric model, the interactions between equal particles are the same (εDD=εLL and σDD=σLL). The interaction between D and L particles is changed by εDL=eεDD and σDL=sσDD. The parameters e and s represent interaction strength and distance, respectively, as deviations from the Lorentz–Berthelot mixing rules. Gibbs energies were calculated to determine the stable crystal structure as a function of e and s, separately. This resulted in demixing for e<0.93 and solid solutions for e>1, with a weak transition to a substitutionally ordered fcc at e>1.8. Variation of s resulted in various crystal structures: a CsCl structure for 0.8<s⩽0.95, NaCl structure for 0.6⩽s⩽0.8, ZnS structures with gradual transition to a double fcc structure for s<0.6. We conclude that small variations in the interactions between unlike particles in a mixture suffice to change the crystal structure completely.