diff --git a/openeo/rest/connection.py b/openeo/rest/connection.py
index 3e5e1f6bf..58b9c7edf 100644
--- a/openeo/rest/connection.py
+++ b/openeo/rest/connection.py
@@ -1132,12 +1132,10 @@ def _build_request_with_process_graph(self, process_graph: Union[dict, Any], **k
         """
         result = kwargs
         process_graph = as_flat_graph(process_graph)
-        if self._api_version.at_least("1.0.0"):
-            if "process_graph" not in process_graph:
-                process_graph = {"process_graph": process_graph}
-            result["process"] = process_graph
-        else:
-            result["process_graph"] = process_graph
+        assert self._api_version.at_least("1.0.0")
+        if "process_graph" not in process_graph:
+            process_graph = {"process_graph": process_graph}
+        result["process"] = process_graph
         return result
 
     # TODO: unify `download` and `execute` better: e.g. `download` always writes to disk, `execute` returns result (raw or as JSON decoded dict)
diff --git a/tests/rest/test_connection.py b/tests/rest/test_connection.py
index ab589c63a..b60f0bf88 100644
--- a/tests/rest/test_connection.py
+++ b/tests/rest/test_connection.py
@@ -1967,18 +1967,6 @@ def test_default_timeout(requests_mock):
     assert conn.get("/foo", timeout=5).json() == '5'
 
 
-def test_execute_042(requests_mock):
-    requests_mock.get(API_URL, json={"api_version": "0.4.2"})
-    conn = Connection(API_URL)
-    with mock.patch.object(conn, "request") as request:
-        conn.execute({"foo1": {"process_id": "foo"}})
-    assert request.call_args_list == [
-        mock.call(
-            "post", path="/result", allow_redirects=False, expected_status=200,
-            json={"process_graph": {"foo1": {"process_id": "foo"}}}
-        )
-    ]
-
 
 @pytest.mark.parametrize("pg", [
     {"foo1": {"process_id": "foo"}},
diff --git a/tests/test_usecase1.py b/tests/test_usecase1.py
index 69cbb7de0..4f3e1bcd2 100644
--- a/tests/test_usecase1.py
+++ b/tests/test_usecase1.py
@@ -9,7 +9,10 @@
 
 @requests_mock.mock()
 class TestUsecase1(TestCase):
-    _capabilities = {"api_version": "0.4.0", "endpoints": [{"path": "/credentials/basic", "methods": ["GET"]}]}
+    _capabilities = {
+        "api_version": "1.0.0",
+        "endpoints": [{"path": "/credentials/basic", "methods": ["GET"]}],
+    }
 
     def setUp(self):
         # configuration phase: define username, endpoint, parameters?