An electrical connector with reduced cross talk and controlled impedance. The connector comprises hybrid shields with lossy portions and conductive portions. The synergistic effect of the lossy portions and the conductive portions allows the hybrid shields to be relatively thin such that they can be incorporated into the mating interface regions or other mechanically constrained regions of the connector to provide adequate crosstalk suppression without undesirably impacting impedance. The conductive portions may be shaped to preferentially position the conductive regions adjacent signal conductors susceptible to cross talk to further contribute to the synergy. The conductive regions may include holes to contribute to desired electrical properties for the connector.