I would like to mention here several improvements or additional results to the paper ‘On randomly weighted one-sided ergodic Hilbert transforms’. We obtained there that iid random weights in L log L are universally good for the almost sure convergence of the weighted one-sided ergodic Hilbert transform for any Dunford–Schwartz operator in a probability space $(X,\Sigma, \mu)$ and any function g satisfying $\int_X |g|{\rm log}^+|g| \,d\mu<+\infty$.