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Supersymmetric models with an inverted mass hierarchy (IMH: multi-TeV firstand second generation matter scalars, and sub-TeV third generation and Higgsscalars) have been proposed to ameliorate phenomenological problems arisingfrom flavor changing neutral currents (FCNCs) and CP violating processes, whilesatisfying conditions of naturalness. Models with an IMH already in place atthe GUT scale have been shown to be constrained in that for many modelparameter choices, the top squark squared mass is driven to negative values. Wedelineate regions of parameter space where viable models with a GUT scale IMHcan be generated. We find that larger values of GUT scale first and secondgeneration scalar masses act to suppress third generation scalars, leading toacceptable solutions if GUT scale gaugino masses are large enough. We showexamples of viable models and comment on their characteristic features. Forexample, in these models the gluino mass is bounded from below, and effectivelydecouples, whilst third generation scalars remain at sub-TeV levels. Whilepossibly fulfilling criteria of naturalness, these models present challengesfor detection at future pp and e^+e^- collider experiments.Comment: 16 page REVTEX file with 6 PS figure

Viable supersymmetric models with an inverted scalar mass hierarchy at the grand unified theory scale