Capture-recapture methods are essential for estimating hidden populations in fields such as public health and the social sciences. Traditional estimators based on the Poisson distribution often underestimate population sizes when the data exhibit overdispersion. To address this limitation, this study introduced the Zelterman-type and MantelHaenszel-type estimators within the zero-truncated discrete Lindley distribution. The conditional technique was utilized for variance estimation. The performance of the proposed estimators was assessed through simulation studies using one-inflated Poisson data across varying population sizes and inflation levels. The results showed that the proposed estimators outperformed traditional Poisson and geometric-based methods, yielding lower relative bias (RBias) and relative root mean square error (RRMSE). Reallife applications further validated these findings, where the Zelterman-type estimator produced near-exact results for golf tees data, (𝑁̂𝑍𝑇=250.42, SE=22.90) compared to estimators from Poisson and geometric. The Mantel-Haenszel-type estimator proved effective in estimating undetected cases, particularly where traditional models were ineffective. Further findings show that the Zelterman-type estimator performs best on data that are highly right-skewed, slightly platykurtic, or leptokurtic, while the MantelHaenszel-type estimator performs better on moderately right-skewed data. In conclusion, the proposed estimator can serve as an alternative estimator in situations where the traditional estimators have failed.