Quantitative ultrasound has shown potential of improving medical diagnosis. In this work, a regularized power law (RPL) for the joint estimation of backscatter coefficient (BSC) and attenuation coefficient (AC) parameters was derived and tested with simulated phantoms and in vivo. For the RPL method, a total variation regularization term regarding the BSC and AC parameters were used. The results were compared with ground truth simulated values. An improvement of precision can be appreciated without compromising the accuracy by factor of 80% and 54% according to bias and coefficient of variation, respectively. The in vivo experiments showed comparable results of the algorithm with the literature (i.e. fibroadenoma:1.90 ± 0.31dB.cm-1.MHz-1, normal tissue: 0.62 ± 0.20dB.cm-1.MHz-1). The results suggest the RPL method has the potential to accurately and precisely estimating BSCs and ACs.