Synthetic spectra generated with the parameterized supernova synthetic-spectrum code SYNOW are compared to photospheric-phase spectra of Type Ib supernovae (SNe Ib). Although the synthetic spectra are based on many simplifying approximations, including spherical symmetry, they account well for the observed spectra. Our sample of SNe Ib obeys a tight relation between the velocity at the photosphere, as determined from the Fe II features, and the time relative to that of maximum light. From this we infer that the masses and the kinetic energies of the events in this sample were similar. After maximum light the minimum velocity at which the He I features form usually is higher than the velocity at the photosphere, but the minimum velocity of the ejected helium is at least as low as 7000 kms. Previously unpublished spectra of SN 2000H reveal the presence of hydrogen absorption features, and we conclude that hydrogen lines also were present in SNe 1999di and 1954A. Hydrogen appears to be present in SNe Ib in general, although in most events it becomes too weak to identify soon after maximum light. The hydrogen-line optical depths that we use to fit the spectra of SNe 2000H, 1999di, and 1954A are not high, so only a mild reduction in the hydrogen optical depths would be required to make these events look like typical SNe Ib. Similarly, the He I line optical depths are not very high, so a moderate reduction would make SNe Ib look like SNe Ic.

21 pages and 24 figures, submitted to ApJ