  Suppose that $(M,\mathfrak{g})$ is a compact Riemannian manifold with
strictly negative sectional curvatures. A subset of conjugacy classes $E
\subset \text{conj}(\pi_1(M))$ is called spectrally rigid if when two
negatively curved Riemannian metrics $\mathfrak{g}_1, \mathfrak{g}_2$ on $M$
have the same marked length spectrum on $E$, then their marked length spectra
coincide everywhere. In this work we show that there are arbitrarily sparse
spectrally rigid sets and that they exist, in some sense, in every direction in
$\pi_1(M)$.
