  We investigate upper bounds for the spectral ratios and gaps for the Steklov
eigenvalues of balls with revolution-type metrics. We do not impose conditions
on the Ricci curvature or on the convexity of the boundary. We obtain optimal
upper bounds for the Steklov spectral ratios in dimensions 3 and higher. In
dimension 3, we also obtain optimal upper bounds for the Steklov spectral gaps.
By imposing additional constraints on the metric, we obtain upper bounds for
the Steklov spectral gaps in dimensions 4 and higher.
