Attenuation imaging using spectral techniques such as the spectral log difference (SLD) method suffers from a severe trade-off between spatial resolution and estimation variance. Recently, the regularized spectral log difference (RSLD) method was proposed as a technique that extends such trade-off by incorporating spatial priors (i.e., total variation) in the inversion process. However, the reduction of the variance of attenuation images could also be accomplished by post-processing of the attenuation maps using noise reduction techniques. The main goal of this study is to determine which strategy (i.e., noise handling during or after the attenuation image reconstruction) provides attenuation maps of better quality, both with synthetic data and experimental data obtained from calibrated physical phantoms. The results suggest that the noise rejection mechanism of RSLD significantly outperforms post-processing SLD images by filtering, nearly doubling the contrast-to-noise ratio for comparable values of estimation bias.