  We discuss several aspects of state-of-the-art calculations of radiative
electroweak symmetry breaking in supergravity models. These models have a
five-dimensional parameter space in contrast with the 21-dimensional one of the
MSSM. We examine the Higgs one-loop effective potential $V_1=V_0+\Delta V$, in
particular how its renormalization-scale ($Q$) independence is affected by the
approximations used to calculate $\Delta V$ and by the presence of a
Higgs-field-independent term which makes $V_1(0)\not=0$. We show that the
latter must be subtracted out to achieve $Q$-independence. We also discuss our
own approach to the exploration of the five-dimensional parameter space and the
fine-tuning constraints within this approach. We apply our methods to the
determination of the allowed region in parameter space of two models which we
argue to be the prototypes for conventional (SSM) and string (SISM) unified
models. To this end we impose the electroweak breaking constraint by minimizing
the one-loop effective potential and study the shifts in $\mu$ and $B$ relative
to the values obtained using the tree-level potential. These shifts are most
significant for small values of $\mu$ and $B$, and induce corresponding shifts
on the lightest $\mu$- and/or $B$-dependent particle masses, \ie, those of the
lightest stau, neutralino, chargino, and Higgs boson states. Finally, we
discuss the predictions for the squark, slepton, and one-loop corrected Higgs
boson masses.
