  We compute the big bang nucleosynthesis limit on the number of light neutrino
degrees of freedom in a model-independent likelihood analysis based on the
abundances of He4 and Li7. We use the two-dimensional likelihood functions to
simultaneously constrain the baryon-to-photon ratio and the number of light
neutrinos for a range of He4 abundances $Y_p$ = 0.225 -- 0.250, as well as a
range in primordial Li7 abundances from (1.6 to 4.1) $ \times 10^{-10}$. For
(Li7/H)$_p = 1.6 \times 10^{-10}$, as can be inferred from the Li7 data from
Population II halo stars, the upper limit to $N_\nu$ based on the current best
estimate of the primordial He4 abundance of $Y_p = 0.238$, is $N_\nu < 4.3$ and
varies from $N_\nu < 3.3$ (at 95% C.L.) when $Y_p=0.225$ to $N_\nu < 5.3$ when
$Y_p=0.250$. If Li7 is depleted in these stars the upper limit to $N_\nu$ is
relaxed. Taking (Li7/H)$_p = 4.1 \times 10^{-10}$, the limit varies from $N_\nu
< 3.9$ when $Y_p = 0.225$ to $N_\nu \la 6$ when $Y_p = 0.250$. We also consider
the consequences on the upper limit to $N_\nu$ if recent observations of
deuterium in high-redshift quasar absorption-line systems are confirmed.
