  The classification of map-germs up to the natural right-left equivalence
(also known as A-equivalence) is often complicated. Certainly it is more
complicated than K-equivalence which is extremely easy to work with because the
associated tangent spaces are not 'mixed' modules as they are in the
A-equivalence case.
  In this paper we use a version of K-equivalence, denoted $_V$K-equivalence,
that is defined using K-equivalences that preserve a variety in the source of
maps to classify maps up to A-equivalence. This is possible through making
clear the connection between the two equivalences - previous work by Damon
mostly focussed on the relation between the codimensions associated to the
maps.
  To demonstrate the power and efficiency of the method we give a
classification of certain A$_e$-codimension 2 maps from $n$-space to
$n+1$-space. The proof using $_V$K-equivalence is considerably shorter - by a
wide margin - than one using A-equivalence directly.
