  Call and Silverman introduced the canonical height associated to a polarized
dynamical system, that is, an endomorphism of a projective variety and an ample
line bundle which pulls back to a tensor power of itself. They also presented
an asymptotic for the variation of this height in a family over a
one-dimensional base in terms of the height on the generic fibre and the height
of the parameter. Here we improve this asymptotic, saving a power in the error
term. As a corollary, we give an explicit bound on the height of parameters at
which the dynamical system specialized to a finite orbit, in the case of
endomorphisms of projective space over the projective line.
