We study models in which soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, Min, above the GUT scale, MGUT. We assume that the scalar masses and gaugino masses have common values, m0 and m1/2 respectively, at Min. We use the renormalisation-group equations of the minimal supersymmetric SU(5) GUT to evaluate their evolutions down to MGUT, studying their dependences on the unknown parameters of the SU(5) superpotential. After displaying some generic examples of the evolutions of the soft supersymmetry-breaking parameters, we discuss the effects on physical sparticle masses in some specific examples. We note, for example, that near-degeneracy between the lightest neutralino and the lighter stau is progressively disfavoured as Min increases. This has the consequence, as we show in (m1/2,m0) planes for several different values of tan β, that the stau-coannihilation region shrinks as Min increases, and we delineate the regions of the (Min,tan β) plane where it is absent altogether. Moreover, as Min increases, the focus-point region recedes to larger values of m0 for any fixed tan β and m1/2. We conclude that the regions of the (m1/2,m0) plane that are commonly favoured in phenomenological analyses tend to disappear at large Min.