[en] SPECT quantitation and image contrast are degraded by photon scatter. Water equivalent depths (WEDs) have been used by several investigators to model scatter responses in non-uniform attenuators. The drawback of this approach is the occurrence of undesired fluctuations in the shape of the scatter responses, as is shown by measurements. An improvement of the WED method is presented, based on the assumption that only a part of the scattering object (the region in the 'scatter cone') contributes significantly to the detected scatter events. The remaining part of the object is treated as a uniform medium. The extension of the WED method with extra-conical invariance (WED_ECI) is evaluated by projection measurements of a phantom with a ^99mTc source. Shapes of scatter responses predicted by the WED_ECI method are found to agree better with the measurements than t hose predicted by conventional WEDs. (author)