diff --git a/pageserver/src/http/routes.rs b/pageserver/src/http/routes.rs
index eb0a04c6c40d..faa20e436e2a 100644
--- a/pageserver/src/http/routes.rs
+++ b/pageserver/src/http/routes.rs
@@ -1806,16 +1806,16 @@ async fn timeline_offload_handler(
             active_timeline_of_active_tenant(&state.tenant_manager, tenant_shard_id, timeline_id)
                 .await?;
 
-        let has_no_unarchived_children = tenant.timeline_has_no_unarchived_children(timeline_id);
+        let has_no_attached_children = tenant.timeline_has_no_attached_children(timeline_id);
         let can_offload = timeline.can_offload();
-        match (can_offload, has_no_unarchived_children) {
+        match (can_offload, has_no_attached_children) {
             (true, true) => {
                 offload_timeline(&tenant, &timeline)
                     .await
                     .map_err(ApiError::InternalServerError)?;
             }
             (_, _) => {
-                let msg = format!("no way to offload timeline, can_offload={can_offload}, has_no_unarchived_children={has_no_unarchived_children}");
+                let msg = format!("no way to offload timeline, can_offload={can_offload}, has_no_attached_children={has_no_attached_children}");
                 return Err(ApiError::PreconditionFailed(msg.into_boxed_str()));
             }
         }
diff --git a/pageserver/src/tenant.rs b/pageserver/src/tenant.rs
index a76695686c30..50cb931d7c98 100644
--- a/pageserver/src/tenant.rs
+++ b/pageserver/src/tenant.rs
@@ -2221,7 +2221,7 @@ impl Tenant {
         }
     }
 
-    pub fn timeline_has_no_unarchived_children(&self, timeline_id: TimelineId) -> bool {
+    pub fn timeline_has_no_attached_children(&self, timeline_id: TimelineId) -> bool {
         let timelines = self.timelines.lock().unwrap();
         !timelines
             .iter()
diff --git a/test_runner/regress/test_timeline_archive.py b/test_runner/regress/test_timeline_archive.py
index e7c832cfbc58..99fea1ba13e4 100644
--- a/test_runner/regress/test_timeline_archive.py
+++ b/test_runner/regress/test_timeline_archive.py
@@ -117,41 +117,52 @@ def test_timeline_archive(neon_env_builder: NeonEnvBuilder, shard_count: int):
     )
 
 
-def test_timeline_offloading(neon_env_builder: NeonEnvBuilder):
+@pytest.mark.parametrize("manual_offload", [False, True])
+def test_timeline_offloading(neon_env_builder: NeonEnvBuilder, manual_offload: bool):
     env = neon_env_builder.init_start()
     ps_http = env.pageserver.http_client()
 
+    # Turn off gc and compaction loops: we want to issue them manually for better reliability
+    tenant_id, _timeline = env.neon_cli.create_tenant(
+        conf={
+            "gc_period": "0s",
+            "compaction_period": "0s" if manual_offload else "1s",
+        }
+    )
+
     # Create two branches and archive them
-    parent_timeline_id = env.neon_cli.create_branch("test_ancestor_branch_archive_parent")
+    parent_timeline_id = env.neon_cli.create_branch("test_ancestor_branch_archive_parent", tenant_id = tenant_id)
     leaf_timeline_id = env.neon_cli.create_branch(
-        "test_ancestor_branch_archive_branch1", "test_ancestor_branch_archive_parent"
+        "test_ancestor_branch_archive_branch1", "test_ancestor_branch_archive_parent", tenant_id = tenant_id
     )
 
     ps_http.timeline_archival_config(
-        env.initial_tenant,
+        tenant_id,
         leaf_timeline_id,
         state=TimelineArchivalState.ARCHIVED,
     )
     leaf_detail = ps_http.timeline_detail(
-        env.initial_tenant,
+        tenant_id,
         leaf_timeline_id,
     )
     assert leaf_detail["is_archived"] is True
 
     ps_http.timeline_archival_config(
-        env.initial_tenant,
+        tenant_id,
         parent_timeline_id,
         state=TimelineArchivalState.ARCHIVED,
     )
 
     def parent_offloaded():
-        ps_http.timeline_offload(tenant_id=env.initial_tenant, timeline_id=parent_timeline_id)
+        if manual_offload:
+            ps_http.timeline_offload(tenant_id=tenant_id, timeline_id=parent_timeline_id)
         assert env.pageserver.log_contains(
             f".*{parent_timeline_id}.*offloading archived timeline.*"
         )
 
     def leaf_offloaded():
-        ps_http.timeline_offload(tenant_id=env.initial_tenant, timeline_id=leaf_timeline_id)
+        if manual_offload:
+            ps_http.timeline_offload(tenant_id=tenant_id, timeline_id=leaf_timeline_id)
         assert env.pageserver.log_contains(f".*{leaf_timeline_id}.*offloading archived timeline.*")
 
     wait_until(30, 1, leaf_offloaded)