  The inability of otherwise successful dynamical models to reproduce the ``HBT
radii'' extracted from two-particle correlations measured at the Relativistic
Heavy Ion Collider (RHIC) is known as the ``RHIC HBT Puzzle.'' Most comparisons
between models and experiment exploit the fact that for Gaussian sources the
HBT radii agree with certain combinations of the space-time widths of the
source which can be directly computed from the emission function, without
having to evaluate, at significant expense, the two-particle correlation
function. We here study the validity of this approach for realistic emission
function models some of which exhibit significant deviations from simple
Gaussian behaviour. By Fourier transforming the emission function we compute
the 2-particle correlation function and fit it with a Gaussian to partially
mimic the procedure used for measured correlation functions. We describe a
novel algorithm to perform this Gaussian fit analytically. We find that for
realistic hydrodynamic models the HBT radii extracted from this procedure agree
better with the data than the values previously extracted from the space-time
widths of the emission function. Although serious discrepancies between the
calculated and measured HBT radii remain, we show that a more
``apples-to-apples'' comparison of models with data can play an important role
in any eventually successful theoretical description of RHIC HBT data.
