The classical superconformal actions of branes in adS superspaces have a closed form depending on a matrix M quadratic in fermions, as found in hep-th/9805217. One can gauge-fix the local κ-symmetry using the Killing spinors of the brane in the bulk. We show that in such gauges the superconformal actions are simplified dramatically since M = 0 in all cases. The relation between classical and ga...