Medical studies have shown that EEG of Alzheimer's disease (AD) patients is "slower" (i.e., contains more low-frequency power) and is less complex compared to age-matched healthy subjects. The relation between those two phenomena has not yet been studied, and they are often silently assumed to be independent. In this paper, it is shown that both phenomena are strongly related. Strong correlation between slowing and loss of complexity is observed in two independent EEG datasets: (1) EEG of predementia patients (a.k.a. Mild Cognitive Impairment; MCI) and control subjects; (2) EEG of mild AD patients and control subjects. The two data sets are from different patients, different hospitals and obtained through different recording systems. The paper also investigates the potential of EEG slowing and loss of EEG complexity as indicators of AD onset. In particular, relative power and complexity measures are used as features to classify the MCI and MiAD patients versus age-matched control subjects. When combined with two synchrony measures (Granger causality and stochastic event synchrony), classification rates of 83 (MCI) and 98 (MiAD) are obtained. By including the compression ratios as features, slightly better classification rates are obtained than with relative power and synchrony measures alone. Copyright © 2011 Justin Dauwels et al.