We discuss the parameter spaces of supersymmetry (SUSY) scenarios taking into account the improved Higgs-mass prediction provided by FeynHiggs 2.14.1. Among other improvements, this prediction incorporates three-loop renormalization-group effects and two-loop threshold corrections, and can accommodate three separate mass scales: m q~ (for squarks), mg~ (for gluinos) and m χ~ (for electroweakinos). Furthermore, it contains an improved treatment of the DR ¯ scalar top parameters avoiding problems with the conversion to on-shell parameters, that yields more accurate results for large SUSY-breaking scales. We first consider the CMSSM, in which the soft SUSY-breaking parameters m and m 1 / 2 are universal at the GUT scale, and then sub-GUT models in which universality is imposed at some lower scale. In both cases, we consider the constraints from the Higgs-boson mass M h in the bulk of the (m, m 1 / 2 ) plane and also along stop coannihilation strips where sparticle masses may extend into the multi-TeV range. We then consider the minimal anomaly-mediated SUSY-breaking scenario, in which large sparticle masses are generic. In all these scenarios the substantial improvements between the calculations of M h in FeynHiggs 2.14.1 and FeynHiggs 2.10.0, which was used in an earlier study, change significantly the preferred portions of the models’ parameter spaces. Finally, we consider the pMSSM11, in which sparticle masses may be significantly smaller and we find only small changes in the preferred regions of parameter space.