In this work we propose a detailed EEG epoch selection method and compare epochs with rare and abundant alpha rhythm (AR) of patients with Alzheimer's disease (AD) and normal controls. Epochs were classified as Dominant Alpha Scenario (DAS) and Rare Alpha Scenario (RAS) according to the AR percentage (energy within the 8-13 Hz bandwidth) in O1, O2 and Oz electrodes. Participants were divided into four groups: 17 DAS controls (N1), 15 DAS mild-AD patients (AD1), 12 RAS controls (N2) and 15 RAS mild-AD patients (AD2). We found out that scenario factor (DAS vs. RAS, two-way ANOVA) is significant over a great amount of electrode-bandwidth situations. Furthermore, one-way ANOVA showed significant differences between RAS AD and RAS controls in much more situations as compared to DAS. This is the first study using AD awake EEG reporting the decisive influence of alpha rhythm on epoch selection, where our results revealed that, contrary to what was initially expected, EEG epochs with poor alpha (RAS) discriminate mild AD much better than those presenting richer alpha content (DAS).