  We present numerical tests of the Virtual Element Method (VEM) tailored for
the discretization of a three dimensional Poisson problem with high-order
"polynomial" degree (up to $p=10$). Besides, we discuss possible reasons for
which the method could return suboptimal-wrong error convergence curves. Among
these motivations, we highlight ill-conditioning of the stiffness matrix and
not particularly "clever" choices of the stabilizations. We propose variants of
the definition of face/bulk degrees of freedom, as well as of stabilizations,
which lead to methods that are much more robust in terms of numerical
performances.
