A. The first part of this work uses the algorithm recently detailed in [1] to classify the irreducible weight modules of the minimal model vertex operator algebra L k ( 3 ), when the level k is admissible. These are naturally described in terms of families parametrised by up to two complex numbers. We also determine the action of the relevant group of automorphisms of 3 on their isomorphism classes and compute explicitly the decomposition into irreducibles when a given family's parameters are permitted to take certain limiting values.Along with certain character formulae, previously established in [2], these results form the input data required by the standard module formalism to consistently compute modular transformations and, assuming the validity of a natural conjecture, the Grothendieck fusion coefficients of the admissible-level 3 minimal models. The second part of this work applies the standard module formalism to compute these explicitly when k = − 3 2 . We expect that the methodology developed here will apply in much greater generality.