© 2017 Geophysical Press Ltd. Curvelet deconvolution refers to seismic deconvolution for reflectivity inversion based on curvelet transform. The curvelet transform is a multi-scale and multi-directional transform that can provide a sparse representation of seismic reflectivity. When using this method to model the reflectivity, the signal is represented effectively by large coefficients and random noise is represented by small ones. In this paper, we conduct a comparative study in the context of reflectivity inversion, to investigate the performance of curvelet deconvolution, least-squares method and L p -norm deconvolution. It is shown that by using curvelet deconvolution, the inverted reflectivity profiles have a better signal-to-noise ratio (SNR) and a higher resolution than those obtained by the least-squares method. On the other hand, its results excel those obtained by L p -norm deconvolution in terms of the lateral continuity. Since curvelet deconvolution can offer a trade-off between the sparseness and lateral continuity, we propose an enhanced L p -norm deconvolution by using the result obtained by curvelet deconvolution as the initial model. Numerical results show that the lateral continuity of the inversed reflectivity profile can be further improved by the proposed method.