[en] 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 (∼2 Myr, 160 pc) and Lupus 3 (∼1 Myr, 200 pc), identified in our earlier works. We obtained 34 new spectra (1.5–2.4 μm, R ∼ 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 $T_{\mathrm{e}\mathrm{f}\mathrm{f}}=2800$ K), and an L3 ($T_{\mathrm{e}\mathrm{f}\mathrm{f}}=2200$ K) brown dwarf in Cha-I, with masses below the deuterium-burning limit. Spectroscopic follow-up of our photometric and proper motion candidates in Lupus 3 is almost complete ($><!--\; >\; -->90\mathrm{\%<!--\; \%\; -->}$), and we conclude that there are very few new substellar objects left to be found in this region, down to 0.01–0.02 $M_{\odot <!--\; ???\; -->}$ and $A_V⩽<!--\; ???\; -->5$. The low-mass portion of the mass function in the two clusters can be expressed in the power-law form $dN/dM\propto <!--\; ???\; -->M^{-<!--\; ???\; -->\mathrm{\alpha <!--\; ??\; -->}}$, with $\mathrm{\alpha <!--\; ??\; -->}\sim <!--\; ???\; -->0.7$, 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 of 5%–15% to the total number of Cha-I members.