Beam emittance degradation associated with charge exchange in a solenoid depends not only upon the magnetic field and beam size at charge exchange but also upon the beam's angular momentum at that point. If the average beam angular momentum per particle is small compared to the corresponding rms value, this dependence disappears. If incident and final angular momenta for a cell have the same magnitude, there will be no emittance growth in that cell associated with charge transfer even though the sign of the angular momentum is reversed. Utilization of this effect to reduce emittance growth due to double charge exchange in two separated cells requires either a specially shaped magnetic field at the neutralizer cell or a beam transit time through the initial charge neutralization cell appreciably less than the cyclotron period of the beam in the cell. The length of the focusing region in a neutralizer cell can be increased by shaping its associated magnetic field. The consequent reduction in beam degradation for beams neutralized over that extended region is a function of the initial beam divergence and size separately and not solely a function of initial emittance.