We present a computation of the leading two-loop corrections to the MSSM Higgs boson masses and electroweak symmetry breaking conditions. The computation is performed in the effective potential approach and includes corrections controlled by the third-family Yukawa couplings and the strong gauge coupling. We discuss a renormalisation scheme that avoids unphysically large threshold effects associated with the bottom Yukawa couplings. We also discuss the implementation of our corrections in computer programs that compute the MSSM mass spectrum from a set of unified high-energy boundary conditions.

PACS numbers: 12.60.Jv, 14.80.Cp