Tukey methods [G. M. Jenkins and D. G. Watts, Spectral Analysis and its Applications (Holden-Day, Oakland, CA, 1968)] to the ␦ 18 O anomalies resolves statistically significant (minimum of 80% level) spectral peaks at 12.2-, 8.3-, 5.5-, 3.78-, 2.3-, and 1.7-year periods. The maximum entropy method places these peaks at 11.4, 7.8, 5.5, and 3.5, 2.3, and 1.7 years. 13. We used singular spectrum analysis (SSA) [R. Vautard and M. Ghil, Physica D 35, 395 (1989)] to reconstruct the most energetic modes in the coral record. After the removal of the seasonal cycle and the longterm trend, with a window length of M ϭ 39 years, SSA produces two modes in clean quadrature: modes 1 and 2, with a period of 11.8 years, and modes 3 and 4, with a period of 5.3 years (modes with periods greater than 39 years are unresolved). After the further removal of the decadal and interdecadal modes and with a window length of M ϭ 25 years, two modes emerge in quadrature: modes 1 and 2, with a period of 5.3 years, and modes 3 and 4, with a period of 3.5 years. The quasi-biennial signal emerges in clean quadrature when a 10-year window length is used. Monte Carlo simulations suggest that all of these modes represent statistically significant (at the 95% confidence level) concentrations of variance. More conventional band-pass filtering yields nearly identical patterns.