Many large-scale real-world transport applications have choice sets that are so large as to make model estimation and application computationally impractical. The ability to estimate models on subsets of the alternatives is thus of great appeal, and correction approaches have existed since the late 1970s for the simple multinomial logit (MNL) model. However, many of these models in practice rely on nested logit specifications, for example, in the context of the joint choice of mode and destination. Recent research has put forward solutions for such generalized extreme value (GEV) structures, but these structures remain difficult to apply in practice. This paper puts forward a simplification of the GEV method for use in computationally efficient implementations of nested logit. The good performance of this approach is illustrated with simulated data, and additional insights into sampling error are also provided with different sampling strategies for MNL.