  We introduce a functor from the cube to the Burnside 2-category and prove
that it is equivalent to the Khovanov spectrum given by Lipshitz and Sarkar in
the almost-extreme quantum grading. We provide a decomposition of this functor
into simplicial complexes. This decomposition allows us to compute the homotopy
type of the almost-extreme Khovanov spectra of diagrams without alternating
pairs.
