Substellar Objects in Nearby Young Clusters – SONYC – is a survey program to investigate the frequency and properties of substellar objects in nearby star-forming regions . We present new spectroscopic follow-up of candidate members in Chamaeleon-I ( \sim 2 Myr , 160 pc ) and Lupus 3 ( \sim 1 Myr , 200 pc ) , identified in our earlier works . We obtained 34 new spectra ( 1.5 – 2.4 \mu m , R \sim 600 ) , and identified two probable members in each of the two regions . These include a new probable brown dwarf in Lupus 3 ( NIR spectral type M7.5 and T _ { \mathrm { eff } } = 2800 K ) , and an L3 ( T _ { \mathrm { eff } } = 2200 K ) brown dwarf in Cha-I , with the mass below the deuterium-burning limit . Spectroscopic follow-up of our photometric and proper motion candidates in Lupus 3 is almost complete ( > 90 \% ) , and we conclude that there are very few new substellar objects left to be found in this region , down to 0.01 – 0.02M _ { \odot } and A _ { V } \leq 5 . The low-mass portion of the mass function in the two clusters can be expressed in the power-law form dN / dM \propto M ^ { - \alpha } , with \alpha \sim 0.7 , in agreement with surveys in other regions . In Lupus 3 we observe a possible flattening of the power-law IMF in the substellar regime : this region seems to produce fewer brown dwarfs relative to other clusters . The IMF in Cha-I shows a monotonic behavior across the deuterium-burning limit , consistent with the same power law extending down to 4 – 9 Jupiter masses . We estimate that objects below the deuterium-burning limit contribute of the order 5 - 15 \% to the total number of Cha-I members .