Rhythmic brain activity at low frequencies (<12 Hz) during rest are thought to increase in neurodegenerative disease, but findings in healthy neurocognitive aging are mixed. Here we address two reasons conventional spectral analyses may have led to inconsistent results. First, spectral-power measures are compared to a baseline condition; when resting activity is the signal of interest, it is unclear what the baseline should be. Second, conventional methods do not clearly differentiate power due to rhythmic versus non-rhythmic activity. The Better OSCillation detection method (BOSC; [10], [65]) avoids these problems by using the signal’s own spectral characteristics as a reference to detect elevations in power lasting a few cycles. We recorded electroencephalographic (EEG) signal during rest, alternating eyes open and closed, in healthy younger (18–25 years) and older (60–74 years) participants. Topographic plots suggested the conventional and BOSC analyses measured different sources of activity, particularly at frequencies, like delta (1–4 Hz), at which rhythms are sporadic (but topographies were more similar in the 8–12 Hz alpha band). There was little theta-band activity meeting the BOSC method’s criteria, suggesting prior findings of theta power in healthy aging may reflect non-rhythmic signal. In contrast, delta oscillations were present at higher levels than theta in both age groups. In sum, applying strict and standardized criteria for rhythmicity, slow rhythms appear present in the resting brain at delta and alpha, but not theta frequencies, and appear unchanged in healthy aging.