Assume that $X_1,\ldots X_m \sim Poi(\lambda_0)$ (iid). Now the goal is to get a worst-case upper bound for $\lambda_0$, which is also consistent when $X_1=...=X_m=0$, or more generally, when $S_m = \sum_{i=1}^m X_i$ is small. The commonly used confidence limit such as Wald limits or limits based on a quantile of the distribution $ \frac{1}{m}Poi(m\cdot \hat{\lambda}_{MLE})$ do not work in this setting, as for instance in the case of $S_m=0$, the upper limit is always zero no matter the sample size $m$.
Therefore, I defined the following worst case estimator given a realization $s_m$ from $S_m$: $$ \hat{\lambda}_{UL}(s_m, p) = \text{argmax}_\lambda \left\{ \lambda : \mathbb{P}_\lambda[S_m \leq s_m] = p \right\}$$
This estimator works well in practice, but I am of course not the first one who came up with this. How are such estimators called in the literature, and are there any high quality sources?