  We revise the problem first addressed by Braunstein and co-workers (Phys.
Rev. Lett. {\bf 83} (5) (1999) 1054) concerning the separability of very noisy
mixed states represented by general density matrices with the form
$\rho_\epsilon = (1-\epsilon)M_d+\epsilon\rho_1$. From a detailed numerical
analysis, it is shown that: (1) there exist infinite values in the interval
taken for the density matrix expansion coefficients, $-1\le
c_{\alpha_1,...,\alpha_N}\le 1$, which give rise to {\em non-physical density
matrices}, with trace equal to 1, but at least one {\em negative} eigenvalue;
(2) there exist entangled matrices outside the predicted entanglement region,
and (3) there exist separable matrices inside the same region. It is also shown
that the lower and upper bounds of $\epsilon$ depend on the coefficients of the
expansion of $\rho_1$ in the Pauli basis. If $\rho_{1}$ is hermitian with trace
equal to 1, but is allowed to have {\em negative} eigenvalues, it is shown that
$\rho_\epsilon$ can be entangled, even for two qubits.
