In this chapter, we propose shrinkage estimators, such as linear shrinkage, preliminary test, shrinkage pretest, Stein, and positive Stein estimators, for improving parameter estimation in the Bell regression model with right-censored data, particularly when dealing with some inactive (nonsignificant) predictors. We develop the asymptotic distributional biases and risks of the proposed estimators. Our numerical exploration, considering various combinations of inactive predictors, censoring constants, and sample sizes, demonstrates the superiority of the proposed estimators over unrestricted estimators. Additionally, we apply these estimators to a real-world scenario, showing that the shrinkage estimators are consistently superior to the unrestricted estimator.