KMT-2016-BLG-2605, with planet-host mass ratio $q=0.012pm 0.001$, has the shortest Einstein timescale, $t_e = 3.41pm 0.13,$days, of any planetary microlensing event to date. This prompts us to examine the full sample of 7 short ($t_e<7,$day) planetary events with good $q$ measurements. We find that six have clustered Einstein radii $theta_e = 115pm 20,muas$ and lens-source relative proper motions $mu_relsimeq 9.5pm 2.5,masyr$. For the seventh, these two quantities could not be measured. These distributions are consistent with a Galactic-bulge population of very low-mass (VLM) hosts near the hydrogen-burning limit. This conjecture could be verified by imaging at first adaptive-optics light on next-generation (30m) telescopes. Based on a preliminary assessment of the sample, planetary companions (i.e., below the deuterium-burning limit) are divided into genuine planets, formed in their disks by core accretion, and very low-mass brown dwarfs, which form like stars. We discuss techniques for expanding the sample, which include taking account of the peculiar anomaly dominated morphology of the KMT-2016-BLG-2605 light curve.
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