  We show that the complement of the coamoeba of a variety of codimension k+1
is k-convex, in the sense of Gromov and Henriques. This generalizes a result of
Nisse for hypersurface coamoebas. We use this to show that the complement of
the nonarchimedean coamoeba of a variety of codimension k+1 is k-convex.
