diff --git a/tests/functional/iceberg/test_incremental_models.py b/tests/functional/iceberg/test_incremental_models.py
index a02d9ffed..f8f1d6b89 100644
--- a/tests/functional/iceberg/test_incremental_models.py
+++ b/tests/functional/iceberg/test_incremental_models.py
@@ -1,4 +1,5 @@
 import pytest
+import time
 
 from pathlib import Path
 
@@ -57,6 +58,8 @@
 
 
 class TestIcebergIncrementalStrategies:
+    append: str = f"append_{hash(time.time())}"
+
     @pytest.fixture(scope="class")
     def project_config_update(self):
         return {"flags": {"enable_iceberg_materializations": True}}
@@ -76,15 +79,11 @@ def setup_class(self, project):
     def models(self):
         return {
             "upstream_table.sql": _MODEL_BASIC_TABLE_MODEL,
-            "append.sql": _MODEL_INCREMENTAL_ICEBERG_APPEND,
+            f"{self.append}.sql": _MODEL_INCREMENTAL_ICEBERG_APPEND,
             "merge.sql": _MODEL_INCREMENTAL_ICEBERG_MERGE,
             "delete_insert.sql": _MODEL_INCREMENTAL_ICEBERG_DELETE_INSERT,
         }
 
-    def test_incremental_strategies_build(self, project, setup_class):
-        run_results = run_dbt()
-        assert len(run_results) == 4
-
     def __check_correct_operations(self, model_name, /, rows_affected, status="SUCCESS"):
         run_results = run_dbt(
             ["show", "--inline", f"select * from {{{{ ref('{model_name}') }}}} where world_id = 4"]
@@ -92,7 +91,7 @@ def __check_correct_operations(self, model_name, /, rows_affected, status="SUCCE
         assert run_results[0].adapter_response["rows_affected"] == rows_affected
         assert run_results[0].adapter_response["code"] == status
 
-        if model_name != "append":
+        if "append" not in model_name:
             run_results, stdout = run_dbt_and_capture(
                 [
                     "show",
@@ -118,9 +117,9 @@ def test_incremental_strategies_with_update(self, project, setup_class):
             )
         )
 
-        run_results = run_dbt(["run", "-s", "append", "merge", "delete_insert"])
+        run_results = run_dbt(["run", "-s", self.append, "merge", "delete_insert"])
         assert len(run_results) == 3
 
-        self.__check_correct_operations("append", rows_affected=3)
+        self.__check_correct_operations(self.append, rows_affected=2)
         self.__check_correct_operations("merge", rows_affected=1)
         self.__check_correct_operations("delete_insert", rows_affected=1)