  We extend the model-independent likelihood analysis of big bang
nucleosynthesis (BBN) based on He4 and Li7 to allow for numbers of degrees of
freedom which differ from the standard model value characterized by $N_\nu =
3$. We use the two-dimensional likelihood functions to simultaneously constrain
the baryon-to-photon ratio and the number of light neutrinos. The upper limit
thus obtained is $N_\nu < 4.0$ (at 95% C.L.). We also consider the consequences
if recent observations of deuterium in high-redshift QSO absorption-line
systems (QSOALS) are confirmed.
