  The Gardner method, traditionally used to generate conservation laws of
integrable equations, is generalized to generate symmetries. The method is
demonstrated for the KdV, Camassa-Holm and Sine-Gordon equations. The method
involves identifying a symmetry which depends upon a parameter; expansion of
this symmetry in a (formal) power series in the parameter then gives the usual
infinite hierarchy of symmetries. We show that the obtained symmetries commute,
discuss the relation of the Gardner method with Lenard recursion (both for
generating symmetries and conservation laws), and also the connection between
the symmetries of continuous integrable equations and their discrete analogs.
