Let $p \in (0, \infty)$ and
${\mathfrak B}_{1}^{p} $ be the class of analytic functions
$f$ in the unit disk ${\mathbb D}$ with $f(0)=0$ satisfying
$|f'(z)| \leq 1/(1-|z|^2)^p$.
For $z_0, z_1 \in {\mathbb D}$,
$w_1 \in {\mathbb C}$ with $z_0 \not= z_1$
and $|w_1| \leq 1/(1-|z_1|^2)^p$,
put $V^p(z_0 ; z_1,w_1) $
be the variability region of $f'(z_0)$ when
$f$ ranges over the class ${\mathfrak B}_1^p$
with $f'(z_1) = w_1$, i.e.,
$V^p(z_0 ; z_1,w_1)
= \{ f'(z_0) : f \in {\mathfrak B}_1^p \; \textrm{and}
\; f'(z_1) = w_1 \}$.
In 1988 M. Bonk showed that $V^1(z_0 ; z_1,w_1) $
is a convex closed Jordan domain and
determined it by giving a parametrization of the simple closed curve
$\partial V^1(z_0 ; z_1,w_1) $.
He also derived distortion theorems for ${\mathfrak B}_{1}^1$ as corollaries.
In the present article we shall
refine Bonk's method and explicitly determine
$V^p(z_0 ; z_1,w_1)$.