Phacoemulsification needles are configured to cause eccentric or wobble-type motion by being formed to distribute the mass of the needle non-uniformly. In one version the non-uniform property is created by angling the needle's aspiration passage with respect to the needle axis. In another, the needle tip walls are formed with non-uniform thicknesses, with or without including an off-axis configuration with respect to the needle aspiration passageway. In another, the needle tip walls are formed in a scalloped configuration. In another, external protuberances or “bumps” are formed on the needle tip exterior wall surfaces. In another, the needle tip walls have weighted inserts placed therein. In another, the needle tip is formed with skewed bevels and ridges. In another, the needle body is formed with non-uniformly shaped segments. In another, a portion of the needle tip is twisted with respect to the rest of the tip.