Iteratively Reweighted Least Squares (IRLS) is a well-established method of optimizing ℓp norm problems such as Total Variation (TV) regularization. Within this general framework, there are several possible ways of constructing the weights and the form of the linear system that is iteratively solved as part of the algorithm. Many of these choices are equally reasonable from a theoretical perspective, and there has, thus far, been no systematic comparison between them. In this paper we provide such a comparison between the main choices in IRLS algorithms for ℓ1- and ℓ2-TV denoising, finding that there is a significant variation in the computational cost and reconstruction quality of the different variants.