  The connection between gauge and Higgs sectors makes supersymmetric
extensions of the Standard Model predictive frameworks for the derivation of
Higgs masses. In this paper, we study the contamination of such predictions by
field-renormalization constants, in the MSSM with two-loop gaugeless
corrections of
$\mathcal{O}{\left(\alpha_{t,b}\,\alpha_s,\,\alpha_{t,b}^2\right)}$ and full
momentum dependence, and demonstrate how strict perturbative expansions allow
to systematically neutralize the dependence on such unphysical objects. On the
other hand, the popular procedure consisting in an iterative pole search
remains explicitly dependent on field counterterms. We then analyze the
magnitude of the intrinsic uncertainty that this feature implies for the
iterative method, both in non-degenerate and near-degenerate regimes, and
conclude that this strategy does not improve on the predictions of the more
straightforward expansion. We also discuss several features related to the
inclusion of the orders $\alpha_{t,b}\,\alpha_s$ and $\alpha_{t,b}^2$ in the
so-called 'fixed-order' approach, such as the resummation of UV-logarithms for
heavy supersymmetric spectra.
