Calculations are performed to demonstrate the deviations from Gaussian that occur in the spectral line profiles of a linear maser as a result of the amplification process. Near-Gaussian profiles are presented for bright, interstellar 22 GHz water masers obtained from high resolution Very Long Baseline Array (VLBA) observations of W3 IRS 5. For the profiles to be so close to Gaussian, the calculations indicate that these masers must originate in quite hot gas with temperatures greater than 1200 K -- a conclusion that is supportive of C-type shocks as the origin of these masers. In addition, the degree of saturation of these masers must be less than approximately one-third, from which it follows that the beaming angles are less than about 10^{-4} ster and the actual luminosities are modest. If spectral profiles that are as close to Gaussian as the profiles presented in this initial investigation are found to occur widely, they can be valuable diagnostics for the environments of astrophysical masers.

4 pages with 3 figures embedded in paper; uses AASTEX with emulateapj5.sty; accepted for publication in ApJ (Letters)