Confinement of charged particles in cylindrical Penning-Malmberg traps depends strongly on cross-magnetic-field transport induced by electric and/or magnetic asymmetries. New measurements in pure-electron plasmas demonstrate two separate transport regimes depending on the particle bounce-to-rotation ratio, or rigidity, R identical with&fmacr;(b)/f(E). For R<10, the transport scales as V(a)R-2, where V(a) is the strength of an applied electrostatic asymmetry. For R greater, similar10-20, this " R-2 transport" ceases abruptly, leaving " B-independent" transport which scales as V(2)(a) and does not depend directly on the rigidity.