  We present a set of formalisms for comparing, evolving and constraining
primordial non-Gaussian models through the CMB bispectrum. We describe improved
methods for efficient computation of the full CMB bispectrum for any general
(non-separable) primordial bispectrum, incorporating a flat sky approximation
and a new cubic interpolation. We review all the primordial non-Gaussian models
in the present literature and calculate the CMB bispectrum up to l <2000 for
each different model. This allows us to determine the observational
independence of these models by calculating the cross-correlation of their CMB
bispectra. We are able to identify several distinct classes of primordial
shapes - including equilateral, local, warm, flat and feature (non-scale
invariant) - which should be distinguishable given a significant detection of
CMB non-Gaussianity. We demonstrate that a simple shape correlator provides a
fast and reliable method for determining whether or not CMB shapes are well
correlated. We use an eigenmode decomposition of the primordial shape to
characterise and understand model independence. Finally, we advocate a
standardised normalisation method for $f_{NL}$ based on the shape
autocorrelator, so that observational limits and errors can be consistently
compared for different models.
