  The constraints proposed recently by Bershadsky to produce $W^l_n$ algebras
are a mixture of first and second class constraints and are degenerate. We show
that they admit a first-class subsystem from which they can be recovered by
gauge-fixing, and that the non-degenerate constraints can be handled by
previous methods. The degenerate constraints present a new situation in which
the natural primary field basis for the gauge-invariants is rational rather
than polynomial. We give an algorithm for constructing the rational basis and
converting the base elements to polynomials.
