Short block copolymers in a selective solvent (bad for A-block, good for B-Mock) are modeled by flexible bead-spring chains, where beads interact with short-range Morse potentials of variable strength. In particular, treating the strength EAA Of attraction between monomers of the A-block as a variable, we study the mass distribution of the micelles that are formed under conditions that correspond to the vicinity of the critical micelle concentration (cmc). Choosing a composition f = N-A/N = (1)/(4) for the block copolymers, we vary their chain length N from N = 4 to N = 32. Only such relatively short chains can be used in thermal equilibrium, since the relaxation times of the system increase dramatically with increasing length. We show that in the regime of parameters accessible to our study, the number of chains per micelle is rather small and almost independent of chain length, implying that the core radius scales as N-A(1)/(3) in this regime. We compare our results with existing theoretical predictions and with experiments.