  This paper revisits a sample of ultracool dwarfs in the Solar neighborhood
previously observed with the Hubble Space Telescope's NICMOS NIC1 instrument.
We have applied a novel high angular resolution data analysis technique based
on the extraction and fitting of kernel phases to archival data. This was found
to deliver a dramatic improvement over earlier analysis methods, permitting a
search for companions down to projected separations of $\sim$1 AU on NIC1
snapshot images. We reveal five new close binary candidates and present revised
astrometry on previously-known binaries, all of which were recovered with the
technique. The new candidate binaries have sufficiently close separation to
determine dynamical masses in a short-term observing campaign. We also present
four marginal detections of objects which may be very close binaries or high
contrast companions. Including only confident detections within 19 parsecs, we
report a binary fraction of at least $\epsilon_b = 17.2^{+5.7}_{-3.7}%$. The
results reported here provide new insights into the population of nearby
ultracool binaries, while also offering an incisive case study of the benefits
conferred by the kernel phase approach in the recovery of companions within a
few resolution elements of the PSF core.
