diff --git a/flepimop/gempyor_pkg/src/gempyor/statistics.py b/flepimop/gempyor_pkg/src/gempyor/statistics.py
index 7b62c608e..3d85c2693 100644
--- a/flepimop/gempyor_pkg/src/gempyor/statistics.py
+++ b/flepimop/gempyor_pkg/src/gempyor/statistics.py
@@ -244,8 +244,8 @@ def llik(self, model_data: xr.DataArray, gt_data: xr.DataArray) -> xr.DataArray:
         """
 
         dist_map = {
-            "pois": lambda ymodel, ydata: -(ymodel + 1)
-            + ydata * np.log(ymodel + 1)
+            "pois": lambda ydata, ymodel: -ymodel
+            + (ydata * np.log(ymodel))
             - gammaln(ydata + 1),
             # >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
             # OLD: # TODO: Swap out in favor of NEW
diff --git a/flepimop/gempyor_pkg/tests/statistics/test_statistic_class.py b/flepimop/gempyor_pkg/tests/statistics/test_statistic_class.py
index 781820165..008b5073d 100644
--- a/flepimop/gempyor_pkg/tests/statistics/test_statistic_class.py
+++ b/flepimop/gempyor_pkg/tests/statistics/test_statistic_class.py
@@ -228,11 +228,87 @@ def simple_valid_resample_and_scale_factory() -> MockStatisticInput:
     )
 
 
+def simple_valid_factory_with_pois() -> MockStatisticInput:
+    data_coords = {
+        "date": pd.date_range(date(2024, 1, 1), date(2024, 1, 10)),
+        "subpop": ["01", "02", "03"],
+    }
+    data_dim = [len(v) for v in data_coords.values()]
+    model_data = xr.Dataset(
+        data_vars={
+            "incidH": (
+                list(data_coords.keys()),
+                np.random.poisson(lam=20.0, size=data_dim),
+            ),
+        },
+        coords=data_coords,
+    )
+    gt_data = xr.Dataset(
+        data_vars={
+            "incidH": (
+                list(data_coords.keys()),
+                np.random.poisson(lam=20.0, size=data_dim),
+            ),
+        },
+        coords=data_coords,
+    )
+    return MockStatisticInput(
+        "total_hospitalizations",
+        {
+            "name": "sum_hospitalizations",
+            "sim_var": "incidH",
+            "data_var": "incidH",
+            "remove_na": True,
+            "add_one": True,
+            "likelihood": {"dist": "pois"},
+        },
+        model_data=model_data,
+        gt_data=gt_data,
+    )
+
+
+def simple_valid_factory_with_pois_with_some_zeros() -> MockStatisticInput:
+    mock_input = simple_valid_factory_with_pois()
+
+    mock_input.config["zero_to_one"] = True
+
+    mock_input.model_data["incidH"].loc[
+        {
+            "date": mock_input.model_data.coords["date"][0],
+            "subpop": mock_input.model_data.coords["subpop"][0],
+        }
+    ] = 0
+
+    mock_input.gt_data["incidH"].loc[
+        {
+            "date": mock_input.gt_data.coords["date"][2],
+            "subpop": mock_input.gt_data.coords["subpop"][2],
+        }
+    ] = 0
+
+    mock_input.model_data["incidH"].loc[
+        {
+            "date": mock_input.model_data.coords["date"][1],
+            "subpop": mock_input.model_data.coords["subpop"][1],
+        }
+    ] = 0
+    mock_input.gt_data["incidH"].loc[
+        {
+            "date": mock_input.gt_data.coords["date"][1],
+            "subpop": mock_input.gt_data.coords["subpop"][1],
+        }
+    ] = 0
+
+    return mock_input
+
+
 all_valid_factories = [
     (simple_valid_factory),
     (simple_valid_resample_factory),
     (simple_valid_resample_factory),
     (simple_valid_resample_and_scale_factory),
+    (simple_valid_factory_with_pois),
+    (simple_valid_factory_with_pois_with_some_zeros),
 ]
 
 
@@ -501,8 +577,21 @@ def test_llik(self, factory: Callable[[], MockStatisticInput]) -> None:
             assert np.allclose(
                 log_likelihood.values,
                 scipy.stats.poisson.logpmf(
-                    mock_inputs.gt_data[mock_inputs.config["data_var"]].values,
-                    mock_inputs.model_data[mock_inputs.config["data_var"]].values,
+                    np.where(
+                        mock_inputs.config.get("zero_to_one", False)
+                        & (mock_inputs.gt_data[mock_inputs.config["data_var"]].values == 0),
+                        1,
+                        mock_inputs.gt_data[mock_inputs.config["data_var"]].values,
+                    ),
+                    np.where(
+                        mock_inputs.config.get("zero_to_one", False)
+                        & (
+                            mock_inputs.model_data[mock_inputs.config["data_var"]].values
+                            == 0
+                        ),
+                        1,
+                        mock_inputs.model_data[mock_inputs.config["data_var"]].values,
+                    ),
                 ),
             )
         elif dist_name in {"norm", "norm_cov"}: