  The deprojection of axisymmetric density distributions is generally
indeterminate to within the addition of certain axisymmetric distributions
(konus densities) that are invisible in projection. The known class of konus
densities is expanded considerably here through the introduction of {\em
semikonus functions}. These functions are closed with respect to multiplication
in ordinary space, and the real part of an arbitrary polynomial of semikonus
functions is a konus function. This property facilitates the construction of
semikonus (and konus) functions with tailored properties, such as asymptotic
forms. We also develop a simple technique for constructing several classes of
konus distributions with arbitrary density profiles in the equatorial plane.
