The laser ablation technique is used to grid-pattern thin Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O crystals to form isolated squares of length scale R. The effect of R on irreversible magnetization and deduced critical currents is studied. The remanent magnetization (Hc) at low temperature is linear within experimental error below a few hundred micrometers, and sublinear at larger sizes. The results are inconsistent with granularity on the scale of the twin boundaries but suggest the presence of some larger-scale defects that impede current flow. In a conventional critical-state model, a field (or flux-density) dependence of the critical current density Jc(h)h-n gives rise to a sublinear size dependence D1/(n+1) of the zero-field remanent magnetization. However, in our geometry, strong demagnetizing fields are expected to curve the flux lines into the plane and reduce the size of this effect. Further evidence for the flux line curvature comes from the fact that the field for the minimum in the virgin curve is almost independent of sample size, in contrast to models that ignore the curvature.