  We examine the space of allowed S-matrices on the Adler zeros' plane using
the recently resurrected (numerical) S-matrix bootstrap program for pion
scattering. Two physical quantities, an averaged total scattering
cross-section, and an averaged entanglement power for the boundary S-matrices,
are studied. Emerging linearity in the leading Regge trajectory is correlated
with a reduction in both these quantities. We identify two potentially viable
regions where the S-matrices give decent agreement with low energy S- and
P-wave scattering lengths and have leading Regge trajectory compatible with
experiments. We also study the line of minimum averaged total cross section in
the Adler zeros' plane. The Lovelace-Shapiro model, which was a precursor to
modern string theory, is given by a straight line in the Adler zeros' plane
and, quite remarkably, we find that this line intersects the space of allowed
S-matrices near both these regions.
