  We deal with planar vortex structures in Maxwell-Higgs models in the presence
of a generalized magnetic permeability. The model under investigation engenders
a real parameter that controls the behavior of the tail of the solutions and of
the quantities associated to them. As the parameter gets larger, the solutions
attain their boundary values faster, unveiling the existence of a peculiar
feature, the presence of double exponential tails. However, the solutions are
not compact so we call them quasi-compact vortices.
