A composite bushing including an outer sleeve coaxially surrounding an inner sleeve, and including an elastomeric body extending between the outer sleeve and the inner sleeve. The elastomeric body is provided with circumferentially alternating wedge sections having different physical characteristics, so as to provide a bushing having directional differences in resistance to deflection. The resiliency in a first radial direction appreciably differs from the resiliency in a second radial direction, where the second radial direction is at an angle to the first radial direction. The resulting bushing configuration can be used to attenuate vibration and noise in a vehicle, and thereby contribute to improved vehicle handling and ride comfort.