KMT-2016-BLG-2605, with planet-host mass ratio q=0.012±0.001, has the shortest Einstein timescale, t\e=3.41±0.13days, of any planetary microlensing event to date. This prompts us to examine the full sample of 7 short (t\e<7day) planetary events with good q measurements. We find that six have clustered Einstein radii θ\e=115±20\muas and lens-source relative proper motions μ\rel≃9.5±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.