As noted by the authors and as stated in our original paper, Universal Inference should not be used in regular problems where more efficient methods are available. Universal Inference is intended for problems where, due to a violation of regularity conditions, no other methods are available. And even in that case, Universal Inference should be thought of a baseline which should be replaced if and when more efficient methods are developed. The power loss is indeed exacerbated when their are nuisance parameters. The confidence sets shrink at the correct rate but the constants can be large. The authors found a very interesting improvement in the Normal case. An interesting future research direction is to see if there is a way to extend their idea to irregular problems. Even when the nuisance parameter is high dimensional, there are cases where Universal Inference is useful. A good example is (Dunn et al.) where Universal inference is used to test if a density is log-concave. Here, the nuisance parameter is infinite dimensional, but Universal Inference performs well. The fact that the variance of the crossfit likelihood ratio (LLR) statistic is infinite in the Normal case is interesting, but its consequences are unclear. First, the right object to study is the logarithm of the split likelihood ratio statistic (LSLR) or its variants. In regular settings, it is the logarithm of the LLR that satisfies (due to the limiting chi-squared distribution) 𝔼[exp(tLLR)] < ∞ for t < 1/2. In a similar vein, we do know that 𝔼[exp(tLSLR)] ≤ 1 for t ≤ 1. We favour averaging over many overlapping splits (the subsampled crossfit approach analysed in the Gaussian Universal Inference Biometrika'23 paper) rather than dividing the data into K chunks.