  The dependence of the sixth equation of Painleve' on its four parameters $(2
\alpha,-2 \beta,2 \gamma,1-2 \delta)
=(\theta_{\infty}^2,\theta_{0}^2,\theta_{1}^2,\theta_{x}^2)$ is holomorphic,
therefore one expects all its Lax pairs to display such a dependence. This is
indeed the case of the second order scalar ``Lax'' pair of Fuchs, but the
second order matrix Lax pair of Jimbo and Miwa presents a meromorphic
dependence on $\theta_\infty$ (and a holomorphic dependence on the three other
$\theta_j$). We analyze the reason for this feature and make suggestions to
suppress it.
