We describe EPIC 205718330 and EPIC 235240266, two systems identified in the K2 data whose light curves contain episodic drops in brightness with shapes and durations similar to those of the young "dipper" stars, yet shallower by ~1-2 orders of magnitude. These "little dippers" have diverse profile shapes with durations of ~0.5-1.0 days and depths of ~0.1-1.0% in flux; however, unlike most of the young dipper stars, these do not exhibit any detectable infrared excess indicative of protoplanetary disks, and our ground-based follow-up spectra lack any signatures of youth while indicating these objects as kinematically old. After ruling out instrumental and/or data processing artifacts as sources of the dimming events, we investigate possible astrophysical mechanisms based on the light curve and stellar properties. We argue that the little dippers are consistent with transits of star-grazing exocomets, and speculate that they are signposts of massive non-transiting exoplanets driving the close-approach orbits.

14 pages, 9 Figures; accepted to MNRAS