  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 mum,
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
Teff=2800 K), and an L3 (Teff=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 - 0.02 MSun and Av \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~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.
