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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 similar to 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 pc, we report a binary fraction of at least epsilon(b) = 17.2(-3.7)(+5.7) %. 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 point-spread function core.