diff --git a/lib/api/model/model.dart b/lib/api/model/model.dart
index b733a1e490..e55dc1d1f0 100644
--- a/lib/api/model/model.dart
+++ b/lib/api/model/model.dart
@@ -656,8 +656,14 @@ enum MessageFlag {
 }
 
 /// The name of a Zulip topic.
-// TODO(#1250): Migrate all implicit uses as String; remove "implements String".
-extension type const TopicName(String _value) implements String {
+// TODO(dart): Can we forbid calling Object members on this extension type?
+//   (The lack of "implements Object" ought to do that, but doesn't.)
+//   In particular an interpolation "foo > $topic" is a bug we'd like to catch.
+// TODO(dart): Can we forbid using this extension type as a key in a Map?
+//   (The lack of "implements Object" arguably should do that, but doesn't.)
+//   Using as a Map key is almost certainly a bug because it won't case-fold;
+//   see for example #739, #980, #1205.
+extension type const TopicName(String _value) {
   /// The string this topic is identified by in the Zulip API.
   ///
   /// This should be used in constructing HTTP requests to the server,
diff --git a/lib/api/model/narrow.dart b/lib/api/model/narrow.dart
index 72a4d7ff77..8082ac64ff 100644
--- a/lib/api/model/narrow.dart
+++ b/lib/api/model/narrow.dart
@@ -28,7 +28,37 @@ ApiNarrow resolveDmElements(ApiNarrow narrow, int zulipFeatureLevel) {
 /// please add more as needed.
 sealed class ApiNarrowElement {
   String get operator;
-  Object get operand;
+
+  /// The operand of this narrow filter.
+  ///
+  /// The base-class getter [ApiNarrowElement.operand] returns `dynamic`,
+  /// and its value should only be used for encoding as JSON, for use in a
+  /// request to the Zulip server.
+  ///
+  /// For any operations that depend more specifically on the operand's type,
+  /// do not use run-time type checks on the value of [operand]; instead, make
+  /// a run-time type check (e.g. with `switch`) on the [ApiNarrowElement]
+  /// itself, and use the [operand] getter of the specific subtype.
+  ///
+  /// That makes a difference because [ApiNarrowTopic.operand] has type
+  /// [TopicName]; at runtime a [TopicName] is indistinguishable from [String],
+  /// but an [ApiNarrowTopic] can still be distinguished from other subclasses.
+  //
+  // We can't just write [Object] here; if we do, the compiler rejects the
+  // override in ApiNarrowTopic because TopicName can't be assigned to Object.
+  // The reason that could be bad is that a caller of [ApiNarrowElement.operand]
+  // could take the result and call Object members on it, like toString, even
+  // though TopicName doesn't declare those members.
+  //
+  // In this case that's fine because the only plausible thing to do with
+  // a generic [ApiNarrowElement.operand] is to encode it as JSON anyway,
+  // which behaves just fine on TopicName.
+  //
+  // ... Even if it weren't fine, in the case of Object this protection is
+  // thoroughly undermined already: code that has a TopicName can call Object
+  // members on it directly.  See comments at [TopicName].
+  dynamic get operand; // see justification for `dynamic` above
+
   final bool negated;
 
   ApiNarrowElement({this.negated = false});