  Given a dissipative operator $A$ on a complex Hilbert space $\mathcal{H}$
such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is
closable, we give a necessary and sufficient condition for an extension of $A$
to still be dissipative. As applications, we describe all maximally accretive
extensions of strictly positive symmetric operators and all maximally
dissipative extensions of a highly singular first-order operator on the
interval.
