  We consider integrable open--boundary conditions for the supersymmetric t--J
model commuting with the number operator $n$ and $S^{z}$. Four families, each
one depending on two arbitrary parameters, are found. We find the relation
between Sklyanin's method of constructing open boundary conditions and the one
for the quantum group invariant case based on Markov traces. The eigenvalue
problem is solved for the new cases by generalizing the Nested Algebraic Bethe
ansatz of the quantum group invariant case (which is obtained as a special
limit). For the quantum group invariant case the Bethe ansatz states are shown
to be highest weights of $spl_{q}(2,1)$.
