  This paper concerns the problem of lifting a KZ doctrine P to the 2-category
of pseudo T-algebras for some pseudomonad T. Here we show that this problem is
equivalent to giving a pseudo-distributive law (meaning that the lifted
pseudomonad is automatically KZ), and that such distributive laws may be simply
described algebraically and are essentially unique (as known to be the case in
the (co)KZ over KZ setting).
  Moreover, we give a simple description of these distributive laws using Bunge
and Funk's notion of admissible morphisms for a KZ doctrine (the principal goal
of this paper). We then go on to show that the 2-category of KZ doctrines on a
2-category is biequivalent to a poset.
  We will also discuss here the case of lifting a locally fully faithful KZ
doctrine, which we noted earlier enjoys most of the axioms of a Yoneda
structure, and show that an oplax-lax bijection is exhibited on the lifted
'Yoneda structure' similar to Kelly's doctrinal adjunction. We also briefly
discuss how this bijection may be viewed as a coherence result for oplax
functors out of the bicategories of spans and polynomials, but leave the
details for a future paper.
