  In a recent paper Dargis and Mathieu introduced integrodifferential odd flows
for the supersymmetric KdV equation. These flows are obtained from the nonlocal
conservation laws associated with the fourth root of its Lax operator. In this
note I show that only half of these flows are of the standard Lax form, while
the remaining half provide us with hamiltonians for an SKdV-type reduction of a
new supersymmetric hierarchy. This new hierarchy is shown to be closely related
to the Jacobian supersymmetric KP-hierarchy of Mulase and Rabin. A detailed
study of the algebra of additional symmetries of this new hierarchy reveals
that it is isomorphic to the super-W_{1+\infty} algebra, thus making it a
candidate for a possible interrelationship between superintegrability and
two-dimensional supergravity.
