  We show how to extend the Covering Spectrum (CS) of Sormani-Wei to two
spectra, called the Extended Covering Spectrum (ECS) and Entourage Spectrum
(ES) that are new for Riemannian manifolds but defined with useful properties
on any metric on a Peano continuum. We do so by measuring in two different ways
the "size" of a topological generalization of the $\delta$-covers of
Sormani-Wei called "entourage covers". For Riemannian manifolds $M$ of
dimension at least 3, we characterize entourage covers as those covers
corresponding to the normal closures of finite subsets of $\pi_{1}(M)$. We show
that CS$\subset$ES$\subset$MLS and that for Riemannian manifolds these
inclusions may be strict, where MLS is the set of lengths of curves that are
shortest in their free homotopy classes. We give equivalent definitions for all
of these spectra that do not actually involve lengths of curves. Of particular
interest are resistance metrics on fractals for which there are no non-constant
rectifiable curves, but where there is a reasonable notion of Laplace Spectrum
(LaS). The paper opens new fronts for questions about the relationship between
LaS and subsets of the length spectrum for a range of spaces from Riemannian
manifolds to resistance metric spaces.
