  Current solar, atmospheric, and reactor neutrino data still allow oscillation
scenarios where the squared mass differences are all close to 10^-3 eV^2,
rather than being hierarchically separated. For solar neutrinos, this situation
(realized in the upper part of the so-called large-mixing angle solution)
implies adiabatic transitions which depend weakly on the neutrino energy and on
the matter density, as well as on the ``atmospheric'' squared mass difference.
In such a regime of ``quasi-energy-independent'' (QEI) transitions,
intermediate between the more familiar ``Mikheyev-Smirnov-Wolfenstein'' (MSW)
and energy-independent (EI) regimes, we first perform analytical calculations
of the solar nu_e survival probability at first order in the matter density,
beyond the usual hierarchical approximations. We then provide accurate,
generalized expressions for the solar neutrino mixing angles in matter, which
reduce to those valid in the MSW, QEI and EI regimes in appropriate limits.
Finally, a representative QEI scenario is discussed in some detail.
