diff --git a/rocketpy/stochastic/stochastic_model.py b/rocketpy/stochastic/stochastic_model.py
index 333a6d891..d42fb76c5 100644
--- a/rocketpy/stochastic/stochastic_model.py
+++ b/rocketpy/stochastic/stochastic_model.py
@@ -124,6 +124,22 @@ def __init__(self, obj, seed=None, **kwargs):
         self.__stochastic_dict = kwargs
         self._set_stochastic(seed)
 
+    def _declare_stochastic_input(self, input_name, input_value):
+        """Declare an input that an ``add_*`` method installs after ``__init__``.
+
+        ``dict_generator`` walks the inputs a model declared rather than every
+        attribute on it (#1109), and that list is built in ``__init__``. Anything
+        added afterwards is set on the instance and never drawn from unless it
+        says so here.
+
+        The value is the argument as given, not the validated form, because
+        ``_set_stochastic`` validates it again on every reseed and binds the
+        distribution to the generator that is live then.
+        """
+        if input_value is None:
+            return
+        self.__stochastic_dict[input_name] = input_value
+
     def _set_stochastic(self, seed=None):
         """Set the stochastic attributes from the input dictionary.
         This method is useful to reset or reseed the attributes of the instance.
diff --git a/rocketpy/stochastic/stochastic_rocket.py b/rocketpy/stochastic/stochastic_rocket.py
index 895e9a2a4..515439f14 100644
--- a/rocketpy/stochastic/stochastic_rocket.py
+++ b/rocketpy/stochastic/stochastic_rocket.py
@@ -457,7 +457,9 @@ def add_cp_eccentricity(self, x=None, y=None):
             Object of the StochasticRocket class.
         """
         self.cp_eccentricity_x = self._validate_eccentricity("cp_eccentricity_x", x)
+        self._declare_stochastic_input("cp_eccentricity_x", x)
         self.cp_eccentricity_y = self._validate_eccentricity("cp_eccentricity_y", y)
+        self._declare_stochastic_input("cp_eccentricity_y", y)
         return self
 
     def add_thrust_eccentricity(self, x=None, y=None):
@@ -485,9 +487,11 @@ def add_thrust_eccentricity(self, x=None, y=None):
         self.thrust_eccentricity_x = self._validate_eccentricity(
             "thrust_eccentricity_x", x
         )
+        self._declare_stochastic_input("thrust_eccentricity_x", x)
         self.thrust_eccentricity_y = self._validate_eccentricity(
             "thrust_eccentricity_y", y
         )
+        self._declare_stochastic_input("thrust_eccentricity_y", y)
         return self
 
     def _validate_eccentricity(self, eccentricity, position):
diff --git a/tests/unit/stochastic/test_stochastic_rocket.py b/tests/unit/stochastic/test_stochastic_rocket.py
index d15eb0bb6..dcf94df36 100644
--- a/tests/unit/stochastic/test_stochastic_rocket.py
+++ b/tests/unit/stochastic/test_stochastic_rocket.py
@@ -1,3 +1,5 @@
+from numbers import Real
+
 import numpy as np
 import pytest
 
@@ -191,3 +193,46 @@ def test_add_free_form_fins_wraps_a_deterministic_fin_set(calisto_robust):
     added = stochastic.aerodynamic_surfaces.get_tuple_by_type(StochasticFreeFormFins)
     assert len(added) == 1
     assert added[0].component.obj is fins
+
+
+@pytest.mark.parametrize(
+    "add_them, names",
+    [
+        (
+            "add_cp_eccentricity",
+            ("cp_eccentricity_x", "cp_eccentricity_y"),
+        ),
+        (
+            "add_thrust_eccentricity",
+            ("thrust_eccentricity_x", "thrust_eccentricity_y"),
+        ),
+    ],
+)
+def test_an_eccentricity_added_after_init_is_still_drawn(calisto, add_them, names):
+    """``dict_generator`` walks the declared inputs, and these arrive later.
+
+    The list is built in ``__init__``, so a distribution installed by an
+    ``add_*`` method afterwards was set on the instance and never drawn from:
+    every simulation used the same value, with nothing to say so.
+    """
+    stochastic = StochasticRocket(rocket=calisto, radius=0.0127 / 2)
+    getattr(stochastic, add_them)(x=(0.0, 0.001), y=(0.0, 0.001))
+    stochastic._set_stochastic(42)
+
+    generated = next(stochastic.dict_generator())
+
+    assert set(names) <= set(generated), f"{add_them} was set but never sampled"
+    assert all(isinstance(generated[name], Real) for name in names)
+
+
+def test_two_seeds_move_an_eccentricity_that_was_added_late(calisto):
+    """Being present is not enough; it has to follow the seed."""
+    stochastic = StochasticRocket(rocket=calisto, radius=0.0127 / 2)
+    stochastic.add_cp_eccentricity(x=(0.0, 0.01), y=(0.0, 0.01))
+
+    def drawn(seed):
+        stochastic._set_stochastic(seed)
+        return next(stochastic.dict_generator())["cp_eccentricity_x"]
+
+    assert drawn(7) == drawn(7)
+    assert drawn(7) != drawn(8)