Acquisition of high-quality land seismic data requires (expensive) dense source and receiver geometries to avoid aliasing-related problems. Alternatively, acquisition using the concept of compressive sensing (CS) allows for similarly high-quality land seismic data using fewer measurements provided that the designed geometry and sparse recovery strategy are well matched. We have developed a complex wavelet-based sparsity-promoting wavefield reconstruction strategy to overcome challenges in land seismic data interpolation using the CS framework. Despite having lower angular sensitivity than curvelets, complex wavelets improve the reconstruction of sparsely acquired land data while being faster and requiring less storage. Unlike the Fourier transform, the complex wavelet transform localizes aliasing-related artifacts likely to be present in field data and yields reconstructions with fewer artifacts and higher signal-to-noise ratios. We determine that the data recovery success depends on the number and the geometry of the missing traces as revealed by analyzing reconstructions from multiple realizations of trace geometry and data decimation ratios. Using half the number of traces required by the regular sampling rules and thus reducing the acquisition costs, we find that data are appropriately reconstructed provided that there are no large gaps in the strategic places.