  The algebra of holomorphic polynomial Sp_{2n}-invariants of k complex 2n by
2n matrices (under diagonal conjugation action) is generated by the traces of
words in these matrices and their symplectic adjoints. No concrete minimal
generating set is known for this algebra apart from the cases n=1, when
Sp_2=SL_2, and n=2, k=1. We construct such sets in the cases n=k=2 and n=3,
k=1. In the latter case we also construct a homogeneous system of parameters
and a Hironaka decomposition of the algebra.
