We present the analyses of two short-timescale ( t _ { E } \sim 5 ~ { } { days } ) microlensing events , KMT-2016-BLG-1820 and KMT-2016-BLG-2142 . In both light curves , the brief anomalies were clearly captured and densely covered by the Korea Microlensing Telescope Network survey . From these analyses , we find that both events have small Einstein radii of \theta _ { E } = 0.12 ~ { } { mas } , suggesting that the binary-lens systems are composed of very low-mass components and/or are located much closer to the lensed stars than to Earth . From Bayesian analyses , we find that these binaries have total system masses of 0.043 _ { -0.018 } ^ { +0.043 } ~ { } M _ { \odot } and 0.088 _ { -0.041 } ^ { +0.120 } ~ { } M _ { \odot } , implying that they are well within the very-low-mass regime . The estimated lens-component masses indicate that the binary lenses consist of a giant-planet/brown-dwarf pair ( KMT-2016-BLG-1820 ) , and a dark/faint object pair ( KMT-2016-BLG-2140 ) that are located near the deuterium-burning and hydrogen-burning mass limits , respectively . Both lens systems are likely to be in the Galactic disk with estimated distances of about 6 kpc and 7 kpc . The projected lens-components separations are 1.1 AU and 0.8 AU , and the mass ratios are 0.11 and 0.20 . These prove that the microlensing method is effective to identify these closely-separated very-low-mass binaries having low mass-ratios .