  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.
