Objective. EEG has great potential as a cost-effective screening tool for Alzheimer's disease (AD). However, the specificity of EEG is not yet sufficient to be used in clinical practice. In an earlier study, we presented preliminary results suggesting improved specificity of EEG to early stages of Alzheimer's disease. The key to this improvement is a new method for extracting sparse oscillatory events from EEG signals in the time-frequency domain. Here we provide a more detailed analysis, demonstrating improved EEG specificity for clinical screening of MCI (mild cognitive impairment) patients. Methods. EEG data was recorded of MCI patients and age-matched control subjects, in rest condition with eyes closed. EEG frequency bands of interest were θ (3.5-7.5 Hz), α(1) (7.5-9.5 Hz), α(2) (9.5-12.5 Hz), and β (12.5-25 Hz). The EEG signals were transformed in the time-frequency domain using complex Morlet wavelets; the resulting time-frequency maps are represented by sparse bump models. Results. Enhanced EEG power in the θ range is more easily detected through sparse bump modeling; this phenomenon explains the improved EEG specificity obtained in our previous studies. Conclusions. Sparse bump modeling yields informative features in EEG signal. These features increase the specificity of EEG for diagnosing AD.