The response functions needed for simulating and fitting two-dimensional infrared spectra are described including the distributions of vibrational frequency, anharmonicity, and coupling between vibrators. A simple method that does not involve explicit calculation is introduced to characterize the spectral line narrowing properties of each of the quantum paths contributing to 2D IR. It is shown that the 2D IR spectra need to be collected in both positive and negative frequency quadrants in order to optimize the information needed to evaluate these correlations. Two experimental examples of heterodyned 2D IR (acetone in ethylene glycol and acetylproline-ND2 in D2O) are described where the 2D IR spectra are obtained for both the conventional echo sequence of pulse delays and for the usually nonrephased signal. These two sets of spectra are quite different for both examples, as predicted. The latter exhibits an echo only when there is some anticorrelation between the relevant inhomogeneous distributions.