We confirm the presence of interannual oscillations of period about 5.9 and 8.5 years in the Earth’s length of day (LOD), better visible after subtracting the atmospheric contribution. Continental water mass redistribution and oceanic angular momentum contribute to a lesser extent, and are furthermore mostly compensated by sea level variations. We show, using a continuous wavelet transform analysis of synthetic oscillators embedded into a random correlated noise, the limits of isolating damped signals presenting nearby periods in time series of limited duration. In particular, we emphasize the possibility that a previously documented 7.3-year oscillation could be an artefact associated with the restricted available time span covered by LOD data. Finally, we perform a wavelet coherence analysis between geodetically observed LOD changes and their prediction from geomagnetically inferred core flow models. It confirms an origin from the fluid outer core for the two signals around 5.9 and 8.5 years. A convincing coherence is also found around 3.5 and 5 years, which may reveal signatures of higher harmonics of torsional modes or of quasi-geostrophic magneto-Coriolis modes.