This paper addresses three important aspects, neglected in all previous literature, of the micromechanics of nanocomposites reinforced by platelet-shaped fillers. (a) A model was developed to predict the buckling of platelets in reinforced materials under compressive loading. This model predicts a critical strain above which platelet buckling, and hence a reduction in the compressive modulus relative to the tensile modulus, would be expected to occur. It was used to show that compressive modulus should not be reduced relative to tensile modulus in a typical polypropylene nanocomposite. (b) A model was developed to account for the reduction of the reinforcement efficiency of clay platelets of high aspect ratio in a polymer matrix as a result of the incomplete exfoliation of platelets into 'pseudoparticle' stacks containing polymer layers sandwiched between successive clay platelet layers rather than into individual perfectly exfoliated and well-dispersed platelets. It was shown that incomplete exfoliation has a very significant detrimental effect on the reinforcement efficiency. (c) A model was also developed for the reduction of the reinforcement efficiency as a result of the deviation of the platelet orientation from perfect biaxial in-plane. It was shown that the deviation of the platelet orientation from perfect biaxial in-plane also has a very significant detrimental effect on the reinforcement efficiency.