We present new upper and lower bounds to the primordial abundances of
deuterium and He-3 based on observational data from the solar system a
nd the interstellar medium. Independent of any model for the primordia
l production of the elements we find (at the 95% C.L.): 1.5 x 10(-5) l
ess than or equal to (D/H)(p) less than or equal to 10.0 x 10(-5) and
(He-3/H)(p) less than or equal to 2.6 x 10(-5). When combined with the
predictions of standard big bang nucleosynthesis, these constraints l
ead to a 95% C.L. bound on the primordial abundance deuterium: (D/H)(b
est) = (3.5(-1.8)(+2.7)) x 10(-5). Measurements of deuterium absorptio
n in the spectra of high-redshift QSOs will directly test this predict
ion. The implications of this prediction for the primordial abundances
of He-4 and Li-7 are discussed, as well as those for the universal de
nsity of baryons.