  We study the class of entire transcendental maps of finite order with one
critical point and one asymptotic value, which has exactly one finite
pre-image, and having a persistent Siegel disc. After normalisation this is a
one parameter family $f_a$ with $a\in\mathbb{C}^*$ which includes the
semi-standard map $\lambda ze^z$ at $a=1$, approaches the exponential map when
$a\to0$ and a quadratic polynomial when $a\to\infty$. We investigate the stable
components of the parameter plane (capture components and semi-hyperbolic
components) and also some topological properties of the Siegel disc in terms of
the parameter.
