  We study constrained versions of the minimal supersymmetric model and
investigate the hierarchy between the electroweak scale and the scale of
superpartners that can be achieved without relying on specifying model
parameters by more than one digit. This approach automatically avoids scenarios
in which a large hierarchy is obtained by special choices of parameters and yet
keeps scenarios that would be otherwise disfavored by various sensitivity
measures. We consider models with universal gaugino and scalar masses, models
with non-universal Higgs masses or non-universal gaugino masses and focus on
scenarios in which all the model parameters are either of the same order or
zero at the grand unification scale. We find that the maximal hierarchy between
the electroweak scale and stop masses, requiring that model parameters are not
specified beyond one digit, ranges from a factor of $\sim 10-30 $ for the CMSSM
up to $\sim 300$ for models with non-universal Higgs or gaugino masses.
