  In this paper, we try to minimize the scope of possible unique metric spectra
up to equivalence. While it is well known that every spectra $S\subseteq
\mathbb{R}^+$ is equivalent to a spectra $T\subseteq \mathbb{N}$, it has
remained open if $T$ could also maintain a desirable combinatorial form. Conant
questioned if $T= \{t_1,...,t_n \}_{<}$ could be taken such that $2^i-1 \leq
t_i \leq 2^n -1$. In this paper, we come to two partial answers. The first is
that the largest element $t_n$ can be chosen such that $t_n\leq 2^n $.
Approximating a full solution, we also observe $T$ with the combinatorial form
$2^i \leq t_i \leq 2^{n+1}$. Our methods are rather unique in the field as we
utilize linear optimization and polygonal geometry to achieve our results. Our
work aims to approach a full characterization of metric spectra, and simplify
future computational endeavors in the field.
