  We present a technique for deriving certain new natural dualities for any
variety of algebras generated by a finite Heyting chain.
  The dualities we construct are tailored to admit a transparent translation to
the more pictorial Priestley/Esakia duality and back again.
  This enables us to combine the two approaches and so to capitalise on the
virtues of both, in particular the categorical good behaviour of a natural
duality: we thereby demonstrate the fullness, or not, of each of our dualities;
we obtain new results on amalgamation; and we also provide a simple treatment
of coproducts.
