diff --git a/hypothesis-python/src/hypothesis/internal/conjecture/data.py b/hypothesis-python/src/hypothesis/internal/conjecture/data.py
index b7d07b32ab..3fc6658e08 100644
--- a/hypothesis-python/src/hypothesis/internal/conjecture/data.py
+++ b/hypothesis-python/src/hypothesis/internal/conjecture/data.py
@@ -1072,9 +1072,17 @@ def __repr__(self):
 
 def ir_value_permitted(value, ir_type, kwargs):
     if ir_type == "integer":
-        if kwargs["min_value"] is not None and value < kwargs["min_value"]:
+        min_value = kwargs["min_value"]
+        max_value = kwargs["max_value"]
+        shrink_towards = kwargs["shrink_towards"]
+        if min_value is not None and value < min_value:
             return False
-        if kwargs["max_value"] is not None and value > kwargs["max_value"]:
+        if max_value is not None and value > max_value:
+            return False
+
+        if (max_value is None or min_value is None) and (
+            value - shrink_towards
+        ).bit_length() >= 128:
             return False
 
         return True
diff --git a/hypothesis-python/tests/conjecture/test_ir.py b/hypothesis-python/tests/conjecture/test_ir.py
index 90f7cf9f05..f403ca4fc6 100644
--- a/hypothesis-python/tests/conjecture/test_ir.py
+++ b/hypothesis-python/tests/conjecture/test_ir.py
@@ -523,9 +523,21 @@ def test_all_children_are_permitted_values(ir_type_and_kwargs):
 @pytest.mark.parametrize(
     "value, ir_type, kwargs, permitted",
     [
-        (0, "integer", {"min_value": 1, "max_value": 2}, False),
-        (2, "integer", {"min_value": 0, "max_value": 1}, False),
-        (10, "integer", {"min_value": 0, "max_value": 20}, True),
+        (0, "integer", {"min_value": 1, "max_value": 2, "shrink_towards": 0}, False),
+        (2, "integer", {"min_value": 0, "max_value": 1, "shrink_towards": 0}, False),
+        (10, "integer", {"min_value": 0, "max_value": 20, "shrink_towards": 0}, True),
+        (
+            int(2**128 / 2) - 1,
+            "integer",
+            {"min_value": None, "max_value": None, "shrink_towards": 0},
+            True,
+        ),
+        (
+            int(2**128 / 2),
+            "integer",
+            {"min_value": None, "max_value": None, "shrink_towards": 0},
+            False,
+        ),
         (
             math.nan,
             "float",