diff --git a/src/relations/tests.rs b/src/relations/tests.rs
index a174475..18cc2d4 100644
--- a/src/relations/tests.rs
+++ b/src/relations/tests.rs
@@ -457,20 +457,23 @@ mod live {
             .expect_err("deleting c's last route to the root should be refused");
         assert_eq!(
             refused.get_status().as_u16(),
-            400,
-            "a stranding delete is a client error, not a server fault: {refused:?}"
+            409,
+            "a stranding delete conflicts with the graph as it stands: {refused:?}"
+        );
+        assert_eq!(
+            refused.problem_slug().as_deref(),
+            Some("would-strand"),
+            "the refusal should say what it is refusing: {refused:?}"
         );
         // With `a` declared root, the victim is unambiguous: `c` is the node that loses its last
         // route. Without a declared root this named a different node between runs, because the
         // projection picked the anchor itself.
-        let message = refused.get_message();
+        let blocked_by = refused.problem().map(|p| p.blocked_by()).unwrap_or_default();
         assert!(
-            message.contains("disconnect"),
-            "the refusal should say what it is refusing: {message}"
-        );
-        assert!(
-            message.contains(c),
-            "the refusal should name {c} as the stranded resource: {message}"
+            blocked_by
+                .iter()
+                .any(|b| b.get("externalId").and_then(serde_json::Value::as_str) == Some(c)),
+            "the refusal should name {c} as the stranded resource: {blocked_by:?}"
         );
 
         // Tear down in one request. Deleting these nodes individually is perfectly legal —
diff --git a/src/timeseries/test.rs b/src/timeseries/test.rs
index 4512a75..b0072d5 100644
--- a/src/timeseries/test.rs
+++ b/src/timeseries/test.rs
@@ -1531,18 +1531,24 @@ mod tests {
             Ok(_) => panic!("Expected 404 Not Found for non-existent timeseries"),
             Err(e) => {
                 assert_eq!(e.get_status(), StatusCode::NOT_FOUND);
-                let msg = e.get_message();
-                assert!(
-                    msg.contains("Could not find following timeseries"),
-                    "unexpected error body: {msg}"
-                );
+                let problem = e.problem().unwrap_or_else(|| panic!("not a problem document: {}", e.get_message()));
+                assert_eq!(problem.slug(), Some("not-found"), "{problem:?}");
+                // `missing` names each series whose data-points were skipped.
+                let named = problem
+                    .extensions
+                    .get("missing")
+                    .and_then(serde_json::Value::as_array)
+                    .is_some_and(|missing| {
+                        missing.iter().any(|m| m.get("externalId").and_then(serde_json::Value::as_str) == Some(missing_ext_id.as_str()))
+                    });
+                assert!(named, "the refusal should name {missing_ext_id}: {problem:?}");
             }
         }
         Ok(())
     }
 
     /// The binary path resolves every series before it builds a frame, so a missing one is
-    /// refused here, with the JSON path's wording, and no frame is ever sent.
+    /// refused here, by the SDK itself, and no frame is ever sent.
     #[tokio::test]
     async fn test_insert_datapoints_binary_missing_timeseries_returns_not_found() -> Result<(), Box<dyn std::error::Error>> {
         let api_service = create_api_service();