  It was asked by Marques-Neves [MN17, Section 9] which min-max p-widths of the
unit 3-sphere lie strictly between $2{\pi}^2$ and $8{\pi}$. We show that the
10th to the 13th widths do.
  More generally, we strengthen X. Zhou's multiplicity one theorem: We prove
that in any closed manifold of dimension between 3 and 7 with a bumpy metric or
a metric of positive Ricci curvature, for any min-max p-width, there exists a
minimizing sequence of sweepouts that only detects multiplicity one minimal
hypersurfaces.
