For a number of bright southern Be stars, high-resolution, high S/N spectroscopy has been performed for Hα, Si II λ6371 and four Fe II emission lines. With the exception of four stars, both Hα and weak emission line profiles exhibit resolved double-peak structure. Peak separation increases with stellar projected rotational velocity. In many cases, Hα profiles (but not Fe II lines) show resolved fine-structure (inflections in the flanks) indicating a two-component structure of the disk. Envelope models with arbitrary density and rotational velocity laws have been fitted to the Fe II line profiles with satisfactory results. It is found that the innermost Hα disk component also emits the Fe II lines and has an average outer radius of 5 r*; density falls off as r-l.5 or more rapidly. The outer disk component emits the faint and narrow secondary component of Hα lines with average outer radius 20 r*. The envelopes of the four stars with a strong, dominating single peak both in Hα and Fe II either are dominated by strong radial motions or, more likely, have elliptical disk-like structure.