Diffusion-ordered spectroscopy experiments in which existing delays in a parent pulse sequence are used for diffusion encoding – iDOSY experiments – are potentially attractive because of their simplicity and sensitivity. However the calculation of diffusional attenuation in Zangger-Sterk pure shift iDOSY experiments is a very difficult problem to attack analytically, and is more easily approached numerically. Numerical simulations show that for typical experimental conditions, the dependence of diffusional attenuation on diffusion-encoding gradient amplitude is well represented by a shifted Gaussian function. The shift in gradient can be calculated analytically for the limiting case where the selective pulse is replaced by a hard 180° pulse at its midpoint; numerical simulations show that the effect of using different shapes of selective pulse is to scale down this limiting gradient shift by a constant factor that depends on the pulse shape used. The practical consequence is that under the experimental conditions appropriate for small molecules, the pure shift iDOSY method should allow good diffusion coefficient measurements to be made if appropriate allowance is made for the change in effective diffusion-encoding gradient. Parallel sets of numerical simulations and experiments are presented, and a practical application of a Zangger-Sterk pure shift iDOSY experiment to a simple test mixture is illustrated.