diff --git a/benchmark/jsonschema.cc b/benchmark/jsonschema.cc
index 3bf15345b..cefcd16bc 100644
--- a/benchmark/jsonschema.cc
+++ b/benchmark/jsonschema.cc
@@ -8,28 +8,14 @@
 #include <sourcemeta/core/jsonschema.h>
 #include <sourcemeta/core/uri.h>
 
-static void Schema_Frame_WoT_Instances(benchmark::State &state) {
+static void Schema_Frame_WoT_References(benchmark::State &state) {
   const auto schema{
       sourcemeta::core::read_json(std::filesystem::path{CURRENT_DIRECTORY} /
                                   "schemas" / "draft7_w3c_wot_td_v1_1.json")};
 
   for (auto _ : state) {
     sourcemeta::core::SchemaFrame frame{
-        sourcemeta::core::SchemaFrame::Mode::Instances};
-    frame.analyse(schema, sourcemeta::core::schema_walker,
-                  sourcemeta::core::schema_resolver);
-    benchmark::DoNotOptimize(frame);
-  }
-}
-
-static void Schema_Frame_OMC_Instances(benchmark::State &state) {
-  const auto schema{
-      sourcemeta::core::read_json(std::filesystem::path{CURRENT_DIRECTORY} /
-                                  "schemas" / "2019_09_omc_json_v2.json")};
-
-  for (auto _ : state) {
-    sourcemeta::core::SchemaFrame frame{
-        sourcemeta::core::SchemaFrame::Mode::Instances};
+        sourcemeta::core::SchemaFrame::Mode::References};
     frame.analyse(schema, sourcemeta::core::schema_walker,
                   sourcemeta::core::schema_resolver);
     benchmark::DoNotOptimize(frame);
@@ -178,8 +164,7 @@ static void Schema_Bundle_Meta_2020_12(benchmark::State &state) {
   }
 }
 
-BENCHMARK(Schema_Frame_WoT_Instances);
-BENCHMARK(Schema_Frame_OMC_Instances);
+BENCHMARK(Schema_Frame_WoT_References);
 BENCHMARK(Schema_Frame_OMC_References);
 BENCHMARK(Schema_Frame_OMC_Locations);
 BENCHMARK(Schema_Frame_ISO_Language_Locations);
diff --git a/src/core/jsonpointer/include/sourcemeta/core/jsonpointer_pointer.h b/src/core/jsonpointer/include/sourcemeta/core/jsonpointer_pointer.h
index cc6eaf338..a3057ece0 100644
--- a/src/core/jsonpointer/include/sourcemeta/core/jsonpointer_pointer.h
+++ b/src/core/jsonpointer/include/sourcemeta/core/jsonpointer_pointer.h
@@ -492,6 +492,55 @@ template <typename PropertyT, typename Hash> class GenericPointer {
     }
   }
 
+  /// Check whether a JSON Pointer starts with another JSON Pointer followed
+  /// by a property token. This is useful for checking container membership
+  /// without allocating a new pointer. For example:
+  ///
+  /// ```cpp
+  /// #include <sourcemeta/core/jsonpointer.h>
+  /// #include <cassert>
+  ///
+  /// const sourcemeta::core::Pointer pointer{"foo", "$defs", "bar"};
+  /// const sourcemeta::core::Pointer prefix{"foo"};
+  /// assert(pointer.starts_with(prefix, "$defs"));
+  /// assert(!pointer.starts_with(prefix, "other"));
+  /// ```
+  template <typename StringT>
+    requires(!std::is_same_v<std::decay_t<StringT>, Token>)
+  [[nodiscard]] auto starts_with(const GenericPointer<PropertyT, Hash> &other,
+                                 const StringT &tail) const -> bool {
+    const auto prefix_size{other.size()};
+    return this->size() > prefix_size && this->starts_with(other) &&
+           this->data[prefix_size].is_property() &&
+           this->data[prefix_size].to_property() == tail;
+  }
+
+  /// Check whether a JSON Pointer starts with another JSON Pointer followed
+  /// by two property tokens. This is useful for checking nested container
+  /// membership without allocating a new pointer. For example:
+  ///
+  /// ```cpp
+  /// #include <sourcemeta/core/jsonpointer.h>
+  /// #include <cassert>
+  ///
+  /// const sourcemeta::core::Pointer pointer{"foo", "$defs", "bar", "baz"};
+  /// const sourcemeta::core::Pointer prefix{"foo"};
+  /// assert(pointer.starts_with(prefix, "$defs", "bar"));
+  /// assert(!pointer.starts_with(prefix, "$defs", "other"));
+  /// ```
+  template <typename StringLeftT, typename StringRightT>
+    requires(!std::is_same_v<std::decay_t<StringLeftT>, Token> &&
+             !std::is_same_v<std::decay_t<StringRightT>, Token>)
+  [[nodiscard]] auto starts_with(const GenericPointer<PropertyT, Hash> &other,
+                                 const StringLeftT &tail_left,
+                                 const StringRightT &tail_right) const -> bool {
+    const auto prefix_size{other.size()};
+    return this->size() > prefix_size + 1 &&
+           this->starts_with(other, tail_left) &&
+           this->data[prefix_size + 1].is_property() &&
+           this->data[prefix_size + 1].to_property() == tail_right;
+  }
+
   /// Check whether a JSON Pointer starts with the initial part of another JSON
   /// Pointer. For example:
   ///
diff --git a/src/core/jsonschema/transformer.cc b/src/core/jsonschema/transformer.cc
index 32287b523..4e297d5c9 100644
--- a/src/core/jsonschema/transformer.cc
+++ b/src/core/jsonschema/transformer.cc
@@ -107,7 +107,7 @@ auto SchemaTransformer::check(
     const std::optional<JSON::String> &default_dialect,
     const std::optional<JSON::String> &default_id) const
     -> std::pair<bool, std::uint8_t> {
-  SchemaFrame frame{SchemaFrame::Mode::Instances};
+  SchemaFrame frame{SchemaFrame::Mode::References};
 
   // If we use the default id when there is already one, framing will duplicate
   // the locations leading to duplicate check reports
@@ -173,7 +173,7 @@ auto SchemaTransformer::apply(
   std::size_t subschema_count{0};
   std::size_t subschema_failures{0};
   while (true) {
-    SchemaFrame frame{SchemaFrame::Mode::Instances};
+    SchemaFrame frame{SchemaFrame::Mode::References};
     frame.analyse(schema, walker, resolver, default_dialect, default_id);
     std::unordered_set<Pointer> visited;
 
diff --git a/src/extension/alterschema/common/orphan_definitions.h b/src/extension/alterschema/common/orphan_definitions.h
index 812a7dc93..0ff2e3e62 100644
--- a/src/extension/alterschema/common/orphan_definitions.h
+++ b/src/extension/alterschema/common/orphan_definitions.h
@@ -15,6 +15,7 @@ class OrphanDefinitions final : public SchemaTransformRule {
             const sourcemeta::core::SchemaWalker &,
             const sourcemeta::core::SchemaResolver &) const
       -> sourcemeta::core::SchemaTransformRule::Result override {
+    ONLY_CONTINUE_IF(schema.is_object());
     const bool has_modern_core{
         vocabularies.contains(Vocabularies::Known::JSON_Schema_2020_12_Core) ||
         vocabularies.contains(Vocabularies::Known::JSON_Schema_2019_09_Core)};
@@ -22,19 +23,41 @@ class OrphanDefinitions final : public SchemaTransformRule {
         vocabularies.contains(Vocabularies::Known::JSON_Schema_Draft_7) ||
         vocabularies.contains(Vocabularies::Known::JSON_Schema_Draft_6) ||
         vocabularies.contains(Vocabularies::Known::JSON_Schema_Draft_4)};
+    const bool has_defs{has_modern_core && schema.defines("$defs")};
+    const bool has_definitions{(has_modern_core || has_draft_definitions) &&
+                               schema.defines("definitions")};
+    ONLY_CONTINUE_IF(has_defs || has_definitions);
 
-    ONLY_CONTINUE_IF(has_modern_core || has_draft_definitions);
-    ONLY_CONTINUE_IF(schema.is_object());
+    const auto prefix_size{location.pointer.size()};
+    bool has_external_to_defs{false};
+    bool has_external_to_definitions{false};
+    std::unordered_set<std::string_view> outside_referenced_defs;
+    std::unordered_set<std::string_view> outside_referenced_definitions;
 
-    std::vector<Pointer> orphans;
+    for (const auto &[key, reference] : frame.references()) {
+      const auto destination_location{frame.traverse(reference.destination)};
+      if (destination_location.has_value()) {
+        if (has_defs) {
+          process_reference(key.second, destination_location->get().pointer,
+                            location.pointer, prefix_size, "$defs",
+                            has_external_to_defs, outside_referenced_defs);
+        }
 
-    if (has_modern_core) {
-      collect_orphans(frame, location, schema, "$defs", orphans);
+        if (has_definitions) {
+          process_reference(key.second, destination_location->get().pointer,
+                            location.pointer, prefix_size, "definitions",
+                            has_external_to_definitions,
+                            outside_referenced_definitions);
+        }
+      }
     }
 
-    if (has_modern_core || has_draft_definitions) {
-      collect_orphans(frame, location, schema, "definitions", orphans);
-    }
+    std::vector<Pointer> orphans;
+    collect_orphans(schema, "$defs", has_defs, has_external_to_defs,
+                    outside_referenced_defs, orphans);
+    collect_orphans(schema, "definitions", has_definitions,
+                    has_external_to_definitions, outside_referenced_definitions,
+                    orphans);
 
     ONLY_CONTINUE_IF(!orphans.empty());
     return APPLIES_TO_POINTERS(std::move(orphans));
@@ -55,19 +78,43 @@ class OrphanDefinitions final : public SchemaTransformRule {
 
 private:
   static auto
-  collect_orphans(const sourcemeta::core::SchemaFrame &frame,
-                  const sourcemeta::core::SchemaFrame::Location &root,
-                  const JSON &schema, const JSON::String &container,
-                  std::vector<Pointer> &orphans) -> void {
-    if (!schema.defines(container) || !schema.at(container).is_object()) {
+  process_reference(const Pointer &source_pointer,
+                    const Pointer &destination_pointer, const Pointer &prefix,
+                    const std::size_t prefix_size, std::string_view container,
+                    bool &has_external,
+                    std::unordered_set<std::string_view> &referenced) -> void {
+    if (!destination_pointer.starts_with(prefix, container) ||
+        destination_pointer.size() <= prefix_size + 1) {
       return;
     }
 
-    for (const auto &entry : schema.at(container).as_object()) {
-      auto entry_pointer{Pointer{container, entry.first}};
-      const auto &entry_location{frame.traverse(root, entry_pointer)};
-      if (frame.instance_locations(entry_location).empty()) {
-        orphans.push_back(std::move(entry_pointer));
+    const auto &entry_token{destination_pointer.at(prefix_size + 1)};
+    if (entry_token.is_property()) {
+      const auto &entry_name{entry_token.to_property()};
+      if (!source_pointer.starts_with(prefix, container)) {
+        has_external = true;
+        referenced.insert(entry_name);
+      } else if (!source_pointer.starts_with(prefix, container, entry_name)) {
+        referenced.insert(entry_name);
+      }
+    }
+  }
+
+  static auto
+  collect_orphans(const JSON &schema, const JSON::String &container,
+                  const bool has_container, const bool has_external_reference,
+                  const std::unordered_set<std::string_view> &referenced,
+                  std::vector<Pointer> &orphans) -> void {
+    if (has_container) {
+      const auto &maybe_object{schema.at(container)};
+      if (maybe_object.is_object()) {
+        // If no external references to container, all definitions are orphans
+        // Otherwise, only unreferenced definitions are orphans
+        for (const auto &entry : maybe_object.as_object()) {
+          if (!has_external_reference || !referenced.contains(entry.first)) {
+            orphans.push_back(Pointer{container, entry.first});
+          }
+        }
       }
     }
   }
diff --git a/test/alterschema/alterschema_lint_2020_12_test.cc b/test/alterschema/alterschema_lint_2020_12_test.cc
index b627c6dd7..91deadf52 100644
--- a/test/alterschema/alterschema_lint_2020_12_test.cc
+++ b/test/alterschema/alterschema_lint_2020_12_test.cc
@@ -6179,6 +6179,88 @@ TEST(AlterSchema_lint_2020_12, orphan_definitions_25) {
   EXPECT_EQ(document, expected);
 }
 
+TEST(AlterSchema_lint_2020_12, orphan_definitions_26) {
+  sourcemeta::core::JSON document = sourcemeta::core::parse_json(R"JSON({
+    "$id": "https://www.sourcemeta.com/schema",
+    "$schema": "https://json-schema.org/draft/2020-12/schema",
+    "properties": {
+      "foo": { "$ref": "#/$defs/bar" }
+    },
+    "$defs": {
+      "bar": {
+        "allOf": [
+          { "$ref": "#/$defs/baz" }
+        ]
+      },
+      "baz": {
+        "type": "object",
+        "properties": {
+          "qux": { "$ref": "#/$defs/extra" }
+        }
+      },
+      "extra": { "type": "string" }
+    }
+  })JSON");
+
+  LINT_AND_FIX(document);
+
+  const sourcemeta::core::JSON expected = sourcemeta::core::parse_json(R"JSON({
+    "$id": "https://www.sourcemeta.com/schema",
+    "$schema": "https://json-schema.org/draft/2020-12/schema",
+    "properties": {
+      "foo": { "$ref": "#/$defs/bar" }
+    },
+    "$defs": {
+      "bar": { "$ref": "#/$defs/baz" },
+      "baz": {
+        "type": "object",
+        "properties": {
+          "qux": { "$ref": "#/$defs/extra" }
+        }
+      },
+      "extra": { "type": "string" }
+    }
+  })JSON");
+
+  EXPECT_EQ(document, expected);
+}
+
+TEST(AlterSchema_lint_2020_12, orphan_definitions_27) {
+  sourcemeta::core::JSON document = sourcemeta::core::parse_json(R"JSON({
+    "$id": "https://www.sourcemeta.com/schema",
+    "$schema": "https://json-schema.org/draft/2020-12/schema",
+    "properties": {
+      "start": { "$ref": "#/$defs/L1" }
+    },
+    "$defs": {
+      "L1": { "allOf": [ { "$ref": "#/$defs/L2" } ] },
+      "L2": { "properties": { "a": { "$ref": "#/$defs/L3" } } },
+      "L3": { "allOf": [ { "$ref": "#/$defs/L4" } ] },
+      "L4": { "properties": { "b": { "$ref": "#/$defs/L5" } } },
+      "L5": { "type": "string" }
+    }
+  })JSON");
+
+  LINT_AND_FIX(document);
+
+  const sourcemeta::core::JSON expected = sourcemeta::core::parse_json(R"JSON({
+    "$id": "https://www.sourcemeta.com/schema",
+    "$schema": "https://json-schema.org/draft/2020-12/schema",
+    "properties": {
+      "start": { "$ref": "#/$defs/L1" }
+    },
+    "$defs": {
+      "L1": { "$ref": "#/$defs/L2" },
+      "L2": { "properties": { "a": { "$ref": "#/$defs/L3" } } },
+      "L3": { "$ref": "#/$defs/L4" },
+      "L4": { "properties": { "b": { "$ref": "#/$defs/L5" } } },
+      "L5": { "type": "string" }
+    }
+  })JSON");
+
+  EXPECT_EQ(document, expected);
+}
+
 TEST(AlterSchema_lint_2020_12,
      unnecessary_allof_wrapper_unevaluated_properties_depends_on_properties) {
   sourcemeta::core::JSON document = sourcemeta::core::parse_json(R"JSON({
diff --git a/test/jsonpointer/jsonpointer_starts_with_test.cc b/test/jsonpointer/jsonpointer_starts_with_test.cc
index 94a094cf5..85d262585 100644
--- a/test/jsonpointer/jsonpointer_starts_with_test.cc
+++ b/test/jsonpointer/jsonpointer_starts_with_test.cc
@@ -130,3 +130,75 @@ TEST(JSONPointer_starts_with, tail_empty_prefix) {
   const sourcemeta::core::Pointer prefix;
   EXPECT_TRUE(pointer.starts_with(prefix, tail));
 }
+
+TEST(JSONPointer_starts_with, property_tail_true) {
+  const sourcemeta::core::Pointer pointer{"foo", "$defs", "bar"};
+  const sourcemeta::core::Pointer prefix{"foo"};
+  EXPECT_TRUE(pointer.starts_with(prefix, "$defs"));
+}
+
+TEST(JSONPointer_starts_with, property_tail_false_wrong_tail) {
+  const sourcemeta::core::Pointer pointer{"foo", "$defs", "bar"};
+  const sourcemeta::core::Pointer prefix{"foo"};
+  EXPECT_FALSE(pointer.starts_with(prefix, "other"));
+}
+
+TEST(JSONPointer_starts_with, property_tail_false_wrong_prefix) {
+  const sourcemeta::core::Pointer pointer{"foo", "$defs", "bar"};
+  const sourcemeta::core::Pointer prefix{"baz"};
+  EXPECT_FALSE(pointer.starts_with(prefix, "$defs"));
+}
+
+TEST(JSONPointer_starts_with, property_tail_pointer_too_short) {
+  const sourcemeta::core::Pointer pointer{"foo"};
+  const sourcemeta::core::Pointer prefix{"foo"};
+  EXPECT_FALSE(pointer.starts_with(prefix, "$defs"));
+}
+
+TEST(JSONPointer_starts_with, property_tail_empty_prefix) {
+  const sourcemeta::core::Pointer pointer{"$defs", "bar"};
+  const sourcemeta::core::Pointer prefix;
+  EXPECT_TRUE(pointer.starts_with(prefix, "$defs"));
+}
+
+TEST(JSONPointer_starts_with, property_tail_index_token) {
+  const sourcemeta::core::Pointer pointer{"foo", 0, "bar"};
+  const sourcemeta::core::Pointer prefix{"foo"};
+  EXPECT_FALSE(pointer.starts_with(prefix, "0"));
+}
+
+TEST(JSONPointer_starts_with, property_two_tails_true) {
+  const sourcemeta::core::Pointer pointer{"foo", "$defs", "bar", "baz"};
+  const sourcemeta::core::Pointer prefix{"foo"};
+  EXPECT_TRUE(pointer.starts_with(prefix, "$defs", "bar"));
+}
+
+TEST(JSONPointer_starts_with, property_two_tails_false_wrong_left) {
+  const sourcemeta::core::Pointer pointer{"foo", "$defs", "bar", "baz"};
+  const sourcemeta::core::Pointer prefix{"foo"};
+  EXPECT_FALSE(pointer.starts_with(prefix, "other", "bar"));
+}
+
+TEST(JSONPointer_starts_with, property_two_tails_false_wrong_right) {
+  const sourcemeta::core::Pointer pointer{"foo", "$defs", "bar", "baz"};
+  const sourcemeta::core::Pointer prefix{"foo"};
+  EXPECT_FALSE(pointer.starts_with(prefix, "$defs", "other"));
+}
+
+TEST(JSONPointer_starts_with, property_two_tails_pointer_too_short) {
+  const sourcemeta::core::Pointer pointer{"foo", "$defs"};
+  const sourcemeta::core::Pointer prefix{"foo"};
+  EXPECT_FALSE(pointer.starts_with(prefix, "$defs", "bar"));
+}
+
+TEST(JSONPointer_starts_with, property_two_tails_empty_prefix) {
+  const sourcemeta::core::Pointer pointer{"$defs", "bar", "baz"};
+  const sourcemeta::core::Pointer prefix;
+  EXPECT_TRUE(pointer.starts_with(prefix, "$defs", "bar"));
+}
+
+TEST(JSONPointer_starts_with, property_two_tails_index_in_right) {
+  const sourcemeta::core::Pointer pointer{"foo", "$defs", 0, "baz"};
+  const sourcemeta::core::Pointer prefix{"foo"};
+  EXPECT_FALSE(pointer.starts_with(prefix, "$defs", "0"));
+}