  In a previous paper, we defined an "elementary" alternative to the ECH
capacities of symplectic four-manifolds, using max-min energy of holomorphic
curves subject to point constraints, and avoiding the use of Seiberg-Witten
theory. In the present paper we use a variant of this construction to define an
alternative to the ECH spectrum of a contact three-manifold. The alternative
spectrum has applications to Reeb dynamics in three dimensions. In particular,
we adapt ideas from a previous joint paper with Edtmair to obtain quantitative
closing lemmas for Reeb vector fields in three dimensions. For the example of
an irrational ellipsoid, we obtain a sharp quantitative closing lemma.
