Under controlled small-amplitude excitation, an initially laminar free shear layer experiences maximum growth rate at a Strouhal number Stθ of 0.017 (consistent with theory) and maximum growth at Stθ ≅ 0.011, while the natural instability frequency Stθn (of an unexcited shear layer) is found to have an intermediate value. Investigations in both axisymmetric and plane shear layers in a number of independent facilities reveal that the Stθn value falls in the range 0.0125-0.0155, depending on the exit boundary-layer fluctuation level and the spanwise radius of curvature. The Stθn value decreases with increasing jet diameter or exit boundary-layer fluctuation level, but is not a direct function of the exit momentum thickness Reynolds number Reθ. For a given facility, the instability details are found to be independent of whether the entrainment at the lip is parallel to the stream or orthogonal (due to the addition of an end plate). The streamwise evolutions of the amplitudes at the fundamental frequency and its harmonics and subharmonics are unique functions of the downstream distance nondimensionalized by the exit momentum thickness, but their details remain functions of the flow geometry (i.e., axisymmetric or plane). Based on data from different facilities, the successive stages of the natural instability have been characterized.