Polymeric micelles composed of asymmetric block copolymers of the type A(n)B(m) in a solvent S are analyzed by the self-consistent-field theory due to Scheutjens and Fleer. Micelle formation is studied in a spherical lattice geometry. An unfavorable mixing of A and S segments drives the self-assembly process, leading to micelles which can vary their aggregation number according to the conditions in solution. We study the micelle thermodynamics and the micelle structure as a function of the solvency of the B tails; the Flory-Huggins interaction parameter chi(SB) has been varied from 0 (good solvent) to 0.5 (Theta solvent). With decreasing solvency the critical micelle volume fraction (CMV) decreases and the micelle size increases. The micelles have a dense core and a more dilute brushlike corona structure. Our main interest is in the density profiles Of the corona. We distinguish four regimes in these profiles, denoted proximal, central, parabolic, and distal. The proximal part of the B profile is near the core and is nonuniversal, the central part is a power law which is in good agreement with the scaling predictions of Daoud and Cotton, in the third regime the profile of the polymer segments is roughly parabolic, and in the distal regime an exponential decay toward the bulk. solution occurs. The relative importance of these regimes depends on the molecular architecture. For example, increasing the number of core (A) segments causes the central part first to grow and then to shrink in favor of the parabolic regime.