This paper presents the comparison of different variance-reduction methods implemented in the Monte Carlo code TRIPOLI-4® in the case of a deep penetration problem. In this complex radiation transport situation, where the shielding is very thick to ensure protection, variance-reduction methods are necessary to obtain results with a good accuracy in a reasonable calculation time. The configuration investigated in this work is a spent-fuel transport cask. The various variance-reduction methods used here consist either of Importance Sampling with the Exponential Transform method, or of sophisticated population-control methods. These methods are detailed, then the results are presented and compared and the efficiency of these methods is investigated. While all methods implemented in TRIPOLI-4® are efficient versus analog simulations, the pre-calculation of importance maps with deterministic methods enables a faster convergence of the Monte Carlo simulations, especially when combined with the Exponential Transform.