  We present synthetic spectral fits of the typical Type Ib SN 1999dn and the
Hydrogen Rich Ib SN 2000H using the generalized non-local thermodynamic
equilibrium stellar atmospheres code \phx. We fit model spectra to five epochs
of SN 1999dn ranging from ten days pre-maximum light to 17 days post-maximum
light and the two earliest epochs of SN 2000H available, maximum light and six
days post-maximum. Our goal is to investigate the possibility of hydrogen in
Type Ib Supernovae (SNe Ib), specifically a feature around 6200\AA\ which has
previously been attributed to high velocity H-alpha. In earlier work on SN
1999dn we found the most plausible alternative to H-alpha to be a blend of Si
II and Fe II lines which can be adjusted to fit by increasing the metallicity.
Our models are simple; they assume a powerlaw density profile with radius,
homologous expansion, and solar compositions. The helium core is produced by
burning 4H --> He in order to conserve nucleon number. For models with hydrogen
the outer skin of the model consists of a shell of solar composition. The
hydrogen mass of the standard solar composition shell is M_H less than about
0.001 times the mass of the sun in SN 1999dn and M_H less than about 0.2 times
the mass of the sun for SN 2000H. Our models fit the observed spectra
reasonably well, successfully reproducing most features including the
characteristic He I absorptions. The hydrogen feature in SN 1999dn is clear,
but much more pronounced in SN 2000H. We discuss a possible evolutionary
scenario that accounts for the dichotomy in the hydrogen shell mass between
these two supernovae.
