The quantitative estimation of the attenuation coefficient slope (ACS) has the potential to differentiate between healthy and pathological tissues. However, attempts to characterize ACS maps using pulse-echo data using methods such as the spectral log difference (SLD) technique have been limited by the large variability of the estimates. In the present work, ACSs were estimated using a regularized SLD technique. The performance of the proposed approach was experimentally evaluated using two physical phantoms: a homogeneous phantom, and a phantom with a cylindrical inclusion. The results obtained with the SLD and regularized SLD techniques were compared to the ACS values obtained with through-transmission techniques. In the homogeneous phantom, the use of regularization allowed reducing the standard deviation by more than 90% while keeping the estimation bias around 2%. For the inhomogenenous phantom, a trade-off between contrast-to-noise ratio (CNR) and estimation bias was observed. However, the use of regularization allowed nearly doubling the CNR from 0.54 to 0.97-1.29 when compared to the standard SLD, while achieving an estimation bias between 10% and 20%. The results suggest that the use of regularization methods can effectively reduce the variability of ACS estimation.