During the first 20 s of its life, the enormous neutrino luminosity of a neutron star drives appreciable mass loss from its surface. This neutrino-driven wind has been previously identified as a likely site for the r-process. Qian & Woosley have derived, both analytically and numerically, the physical conditions relevant for heavy element synthesis in the wind. These conditions include the entropy (S), the electron fraction (Y-e), the dynamic timescale, and the mass loss rate. Here we explore the implications of these conditions for nucleosynthesis. We find that the standard wind models derived in that paper are inadequate to make the r-process, though they do produce some rare species above the iron group. We further determine the general restrictions on the entropy, the electron fraction, and the dynamic timescale that are required to make the r-process. In particular, we derive from nuclear reaction network calculations the conditions required to give a sufficient neutron-to-seed ratio for production of the platinum peak. These conditions range from Y-e approximate to 0.2 and S less than or similar to 100 baryon(-1) for reasonable dynamic timescales of similar to 0.001-0.1 s, to Y-e approximate to 0.4-0.495 and S greater than or similar to 2.400 baryon(-1) for a dynamic timescale of similar to 0.1 s. These conditions are also derived analytically to illustrate the physics determining the neutron-to-seed ratio.