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The study of the dominant population of high redshift IR-luminous galaxies(10^11 - 10^12 Lsun at 1<z<3), requires observation of sources at the ~0.1 mJylevel in the mid-IR. We present the deepest spectra taken to date with theInfrared Spectrograph (IRS) on the Spitzer Space Telescope. We targeted twofaint (f24~0.15 mJy) sources in the Southern GOODS field at z=1.09 and z=2.69.Spectra of the lower redshift target were taken in the observed-frame 8--21micron range, while the spectrum of the higher redshift target covered 21--37microns. We also present the spectra of two secondary sources within the slit.We detect strong PAH emission in all four targets, and compare the spectra tothose of local galaxies observed by the IRS. The z=1.09 source appears to be atypical, star-formation dominated IR-luminous galaxy, while the z=2.69 sourceis a composite source with strong star formation and a prominent AGN. The IRACcolors of this source show no evidence of rest-frame near-infrared stellarphotospheric emission. We demonstrate that an AGN which contributes only asmall (~10%) fraction of the bolometric luminosity can produce enough hot dustemission to overwhelm the near-IR photospheric emission from stars. Suchsources would be excluded from photometric surveys which rely on the near-IRbump to identify starbursts, leading to an underestimate of the star formationrate density.

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