diff --git a/autofit/non_linear/search/nest/dynesty/search/abstract.py b/autofit/non_linear/search/nest/dynesty/search/abstract.py
index 8a3d99f7d..484316e79 100644
--- a/autofit/non_linear/search/nest/dynesty/search/abstract.py
+++ b/autofit/non_linear/search/nest/dynesty/search/abstract.py
@@ -2,6 +2,7 @@
 
 import logging
 import os
+import sys
 from abc import ABC
 from pathlib import Path
 from typing import Dict, Optional, Tuple, Union, TYPE_CHECKING
@@ -397,7 +398,12 @@ def iterations_from(
         if isinstance(self.paths, NullPaths):
             if self.maxcall is not None:
                 return self.maxcall, self.maxcall
-            return int(1e99), int(1e99)
+            # ``sys.maxsize`` rather than ``int(1e99)``: dynesty's dynamic sampler
+            # computes ``maxcall - ncall`` where ``ncall`` is a numpy int64, and a
+            # 99-digit Python int overflows that subtraction (OverflowError:
+            # Python int too large to convert to C long). ``sys.maxsize`` is the
+            # "unbounded" sentinel dynesty itself uses when ``maxcall=None``.
+            return sys.maxsize, sys.maxsize
 
         try:
             total_iterations = np.sum(search_internal.results.ncall)
diff --git a/test_autofit/non_linear/search/nest/test_dynesty.py b/test_autofit/non_linear/search/nest/test_dynesty.py
index 86f72372a..6eaaa2a8b 100644
--- a/test_autofit/non_linear/search/nest/test_dynesty.py
+++ b/test_autofit/non_linear/search/nest/test_dynesty.py
@@ -62,6 +62,29 @@ def test__explicit_params():
     assert search.number_of_cores == 1
 
 
+@pytest.mark.parametrize("search_cls", [af.DynestyStatic, af.DynestyDynamic])
+def test__null_paths_iteration_budget_fits_c_long(search_cls):
+    """
+    Without an output directory (NullPaths) the per-chunk budget is "unbounded".
+    It must be ``sys.maxsize``, not ``int(1e99)``: dynesty's dynamic sampler
+    subtracts a numpy int64 ``ncall`` from it, which raised
+    ``OverflowError: Python int too large to convert to C long``.
+    """
+    import sys
+    from autofit.non_linear.paths.null import NullPaths
+
+    search = search_cls()
+    assert isinstance(search.paths, NullPaths)
+
+    iterations, total = search.iterations_from(MockDynestySampler(results=None))
+
+    assert iterations == total == sys.maxsize
+    assert iterations - np.int64(40) == sys.maxsize - 40
+
+    search = search_cls(maxcall=100)
+    assert search.iterations_from(MockDynestySampler(results=None)) == (100, 100)
+
+
 @pytest.mark.parametrize("search_cls", [af.DynestyStatic, af.DynestyDynamic])
 def test__single_core_builds_no_pool(search_cls, monkeypatch):
     """