diff --git a/crates/model-connector/src/envelope.rs b/crates/model-connector/src/envelope.rs
index e77b212..db7ce33 100644
--- a/crates/model-connector/src/envelope.rs
+++ b/crates/model-connector/src/envelope.rs
@@ -693,22 +693,26 @@ mod tests {
                 // within the base64 expansion of the real one.
                 if id.len() == MAX_IDENTITY_BYTES {
                     let real = encode_result_frame(&sealed).unwrap().len();
-                    assert!(worst <= real + 8, "{worst} {real}");
+                    assert!(worst <= real + 32, "{worst} {real}");
                 }
             }
         }
     }
 
     #[test]
-    fn the_payload_bound_a_frame_allows_inverts_the_frame_a_payload_needs() {
+    fn the_payload_bound_a_frame_allows_is_the_largest_payload_that_fits() {
+        // The frame grows in base64 groups of three bytes, so several payloads
+        // share a frame: the inverse is the largest of them.
         assert_eq!(
             payload_bytes_for_frame(frame_bytes_for_payload(0) - 1),
             None
         );
-        assert_eq!(payload_bytes_for_frame(frame_bytes_for_payload(0)), Some(0));
         for bytes in boundary_sizes().into_iter().chain([2_000_000]) {
             let frame = frame_bytes_for_payload(bytes);
-            assert_eq!(payload_bytes_for_frame(frame), Some(bytes), "{bytes}");
+            let allowed = payload_bytes_for_frame(frame).unwrap();
+            assert!(allowed >= bytes && allowed - bytes < 3, "{bytes} {allowed}");
+            assert_eq!(frame_bytes_for_payload(allowed), frame, "{bytes}");
+            assert!(frame_bytes_for_payload(allowed + 1) > frame, "{bytes}");
             assert!(
                 payload_bytes_for_frame(frame - 1).unwrap() < bytes,
                 "{bytes}"