Background Excessive daytime sleepiness (EDS) is a cause of low quality of life among obstructive sleep apnoea (OSA) patients. Current methods of assessing and predicting EDS are limited due to time constraints or differences in subjective experience and scoring. Electroencephalogram (EEG) power spectral densities (PSDs) have shown differences between OSA and non-OSA patients, and fatigued and non-fatigued patients. Therefore, polysomnographic EEG PSDs may be useful to assess the extent of EDS among patients with OSA. Methods Patients presenting to Israel Loewenstein hospital reporting daytime sleepiness who recorded mild OSA on polysomnography and undertook a multiple sleep latency test. Alpha, beta, and delta relative powers were assessed between patients categorized as non-sleepy (mean sleep latency (MSL) ≥10 min) and sleepy (MSL <10 min). Results 139 patients (74% male) were included for analysis. 73 (53%) were categorized as sleepy (median MSL 6.5 min). There were no significant differences in demographics or polysomnographic parameters between sleepy and non-sleepy groups. In multivariate analysis, increasing relative delta frequency power was associated with increased odds of sleepiness (OR 1.025 (95% CI 1.024–1.026)), while relative alpha and beta powers were associated with decreased odds. The effect size of delta PSD on sleepiness was significantly greater than that of either alpha or beta frequencies. Conclusion Delta PSD during polysomnography is significantly associated with a greater degree of objective daytime sleepiness among patients with mild OSA. Further research is needed to corroborate our findings and identify the direction of potential causal correlation between delta PSD and EDS.