Rheological properties were examined for a butadiene-styrene (BS) diblock copolymer dissolved in an S-selective solvent, dibutyl phthalate (DBP). This copolymer was composed of a deuterated B block (M-B = 13.3 x 10(3)) and a protonated S block (M-S = 53.9 x 10(3)), and the microdomain structure in the quiescent state as well as under steady shear was detected with small-angle neutron scattering (SANS). At 25 degreesC, a quiescently equilibrated BS/DBP system of the BS concentration =28 wt % exhibited elastic behavior under slow, small-amplitude oscillatory shear. This elasticity reflected a bcc lattice of BS micelles with B cores and S corona. Although the B cores were in the liquid state, the thermodynamic power of segregation from the S/DBP phase forced these cores to be arranged on the lattice at equilibrium. Under steady shear, the BS/DBP system exhibited significantly non-Newtonian flow behavior. At low shear rates (gamma )over dot, the steady state was attained after a significant stress overshoot followed by a thixotropic stress decay, and the viscosity eta in this state was proportional to (gamma )over dot(-1). This plastic behavior reflected mild disruption of the micellar lattice (decrease of the grain size) under slow shear. In contrast, at higher (gamma )over dot, the lattice was massively disrupted to exhibit weaker (gamma )over dot dependence of eta. Corresponding to this massive disruption, the BS/DBP system just after cessation of the fast pre-shear exhibited full relaxation (with no equilibrium elasticity) attributed to the B/S concentration fluctuation. This pre-sheared system reformed the micellar lattice to recover its elasticity when kept quiescently, and the slowest reformation/recovery was observed at the pre-shear rate being comparable to the frequency omega (f) of the concentration fluctuation. Thus, the pre-shear at (gamma )over dot similar or equal to omega (f) disrupted the lattice most efficiently (thereby resulting in the slowest lattice reformation). These rheological features and structures of the BS/DBP system were discussed in relation to the softness of the micellar B cores.