The reference PSI Criticality Safety Evaluation (CSE) methodology is based on the frequentist statistics approach and requires derivation of a lower tolerance bound (LTB) for a hypothetical 𝑘_cal / k_bench population, where 𝑘_cal is the calculation 𝑘_𝑒ff (routinely obtained with Monte Carlo (MC) codes) and 𝑘_bench is the experimental benchmark 𝑘_𝑒ff. Nowadays it is possible to quantify the nuclear data (ND) related uncertainties associated with MC 𝑘_𝑒ff calculations with different options including, e.g., Iterated Fission Probability method, as realized in MCNP6®, or stochastic sampling approach, as implemented in the PSI in-house tool NUSS. The question discussed in this paper is how exactly to use the capability of the ND uncertainties quantification (UQ) in the CSE practice, given still existing limitations on the nuclear data evaluations and benchmark specifications sides. This paper presents some NDUQ results, including a correlation analysis for the models of the PSI CSE validation benchmark suite and the preliminary design disposal canister of the Swiss National Cooperative for the Disposal of Radioactive Waste (Nagra) loaded with Swiss used PWR fuel of different burnups. A verification of the NUSS results against analogues MCNP6/Whisper results is shown. After that is described an observation of a Peelle’s Pertinent Puzzle –type problem encountered in the course of the study and finally recommendations for the practical CSE approach are given.