  We study semi-strict tricategories in which the only weakness is in vertical
composition. We construct these as categories enriched in the category of
bicategories with strict functors, with respect to the cartesian monoidal
structure. As these are a form of tricategory it follows that doubly-degenerate
ones are braided monoidal categories. We show that this form of semi-strict
tricategory is weak enough to produce all braided monoidal categories. That is,
given any braided monoidal category $B$ there is a doubly-degenerate
``vertically weak'' semi-strict tricategory whose associated braided monoidal
category is braided monoidal equivalent to $B$.
