  We are concerned with finite-dimensional irreducible representations of the
Yangians associated with the orthosymplectic Lie superalgebras ${\frak
osp}_{2n+1|2m}$. Every such representation is highest weight and we use
embedding theorems and odd reflections of Yangian type to derive necessary
conditions for an irreducible highest weight representation to be
finite-dimensional. We conjecture that these conditions are also sufficient. We
prove the conjecture in the case $n=1$ and arbitrary $m\geqslant 1$.
