The importance of 2D or 3D site effects has been shown by theoretical studies. However, there is a lack of observational evidence of site effects due to lateral heterogeneities. We have evaluated 1D and 2D site effects in the data obtained by a dense seismograph array that operated for more than 2 months in the alluvial basin of Parkway, New Zealand. 1D site effects were evaluated using three independent techniques: spectral ratios relative to a reference station, spectral ratios of horizontal relative to vertical ground motion, and a generalized inversion scheme. Site effects due to lateral heterogeneity were investigated in detail for two events using frequency-wavenumber analysis. Our results show that it is not possible to separate 1D from 2D site effects using frequency-domain techniques. This explains the scatter obtained from standard 1D data analysis: the 1D resonance peaks will be more or less contaminated with laterally propagating waves for different events.