  In May 2012 two asteroids made near-miss "grazing" passes at distances of a
few Earth-radii: 2012 KP24 passed at nine Earth-radii and 2012 KT42 at only
three Earth-radii. The latter passed inside the orbital distance of
geosynchronous satellites. From spectral and imaging measurements using NASA's
3-m Infrared Telescope Facility (IRTF), we deduce taxonomic, rotational, and
physical properties. Their spectral characteristics are somewhat atypical among
near-Earth asteroids: C-complex for 2012 KP24 and B-type for 2012 KT42, from
which we interpret the albedos of both asteroids to be between 0.10 and 0.15
and effective diameters of 20+-2 and 6+-1 meters, respectively. Among B-type
asteroids, the spectrum of 2012 KT42 is most similar to 3200 Phaethon and 4015
Wilson-Harrington. Not only are these among the smallest asteroids spectrally
measured, we also find they are among the fastest-spinning: 2012 KP24 completes
a rotation in 2.5008+-0.0006 minutes and 2012 KT42 rotates in 3.634+-0.001
minutes.
