Abstract Data from eight stellar occultations by Neptune between 1984 and 1988 are analyzed to set limits on the optical depths of the continuous Adams and Le Verrier Rings, and to search for previously unidentified occultations by the arcs in the Adams Ring. We employ the approach introduced by Sicardy et al . (1991), Icarus 89, 220-243) and convert the raw lightcurves to radial profiles of equivalent width E ( r ), the fraction of incident starlight removed by ring material at normal incidence integrated over a specified radial range, or "window." In order to optimize the search for narrow rings, the window length is fixed at 15 km. Radii in Neptune's equatorial plane are calculated using the Neptune pole direction determined by Jacobson et al . (1990), AIAA/AAS Astrodynamics Conference , pp. 157-167). Using data from the occultation of 20 August 1985, we set a 3 σ upper limit of 75 m on the equivalent width of the Adams Ring at a longitude 120° away from tile arc region, near the location of minimum ring brightness in the Voyager images (Showalter and Cuzzi 1994, in preparation). This limit is for a maximum ring width of 15 km; for a maximum ring width of 50 km, the corresponding upper limit is E ≤ 210 m. Combining the results from this data set with similar upper limits obtained by Sicardy et al . (1991) with a 50-km window size, and assuming that the Adams Ring is azimuthally homogeneous away from the arc region, we find that the equivalent width of this ring is ≤90 m at the 90% confidence level, or ≤ 5% of the measured equivalent width of the Egalite arc. A comparison of this result with the relative brightnesses of ring and arcs observed at low phase angles in Voyager images (Showalter and Cuzzi 1994) suggests either that the particles in the Adams Ring have higher albedos than those confined within the arcs, or that the width of the continuous ring significantly exceeds 50 km. The 20 August 1985 lightcurve has also yielded the first tentative earth-based detection of the Le Verrier Ring, with an overall radial width of 135 km and an equivalent width of 520 ± 55 m at λ2.2 μm which are similar to results obtained by the Voyager Photopolarimeter occultation experiment at λ0.27 μm (Horn et al . 1991, Geophys. Res. Lett. 17, 1745-1748). The ratio E PPS / E 2.2 μm = 1.3 ± 0.3. The mean radii of both occultation profiles—53055 and 53125 km, respectively, projected into the ring plane determined by Porco et al . ( Neptune and Triton Conference, Tucson, AZ, 1992 ) and Showalter and Cuzzi (1992), Bull. Am. Astron. Soc. 24, 1029)—are significantly less than the image-derived radius of 53200 ± 20 km (Porco et al . 1992). It is conceivable that this discrepancy could be due to an unrecognized inclination and/or eccentricity. A comparison of our putative detection of the Le Verrier Ring with upper limits set by Sicady et al . (1991) suggests that this ring must be azimuthally inhomogeneous on scales of ∼10°, if our detection is real. A feature in the vicinity of the Adams Ring at the predicted longitude of the Liberte arc was seen in data obtained on 9 July 1988, but a discrepancy of 270 km between the calculated radius and the known semi-major axis of the ring seems to rule out an identification with the arc. Attempts to fit a precessing ellipse model to all available occultation data for the Adams Ring which will also accommodate this observation are in vain. The remaining occultation-derived radii for this ring are found to be consistent with the resonant-perturbation model of Porco (1991, Science 253, 995-1001), and suggest strongly that the Adams Ring lies in, or very close to, Neptune's equatorial plane.