Previously, the noise characteristics obtained with penalized likelihood reconstruction (or maximum-a-posteriori, MAP) have been compared to those obtained with post-smoothed maximum-likelihood (ML) reconstruction, for applications requiring uniform resolution. It was found that penalized-likelihood reconstruction was not superior to post-smoothed ML. In this study a similar comparison is made, but now for applications where the noise suppression is tuned with anatomical information. Our simulations reveal that "straightforward" post-processing of the ML reconstruction results in inferior performance. It is hypothesized that this is due to the noise correlations between neighboring pixels, and an approximate prewhitening filter is derived. The efficacy of the prewhitening filter is illustrated with simulations. When this prewhitening filter was incorporated in the post-processing method, the performance became similar to that of MAP.