diff --git a/model_analyzer/analyzer.py b/model_analyzer/analyzer.py
index a759a6c24..fa7a9c49c 100755
--- a/model_analyzer/analyzer.py
+++ b/model_analyzer/analyzer.py
@@ -84,6 +84,7 @@ def __init__(
         )
 
         self._search_parameters: Dict[str, SearchParameters] = {}
+        self._composing_search_parameters: Dict[str, SearchParameters] = {}
 
     def profile(
         self, client: TritonClient, gpus: List[GPUDevice], mode: str, verbose: bool
@@ -119,6 +120,7 @@ def profile(
         self._create_metrics_manager(client, gpus)
         self._create_model_manager(client, gpus)
         self._populate_search_parameters()
+        self._populate_composing_search_parameters()
 
         if self._config.triton_launch_mode == "remote":
             self._warn_if_other_models_loaded_on_remote_server(client)
@@ -428,9 +430,12 @@ def _populate_search_parameters(self):
                 model.model_config_parameters(),
                 is_bls_model=bool(self._config.bls_composing_models),
             )
+
+    def _populate_composing_search_parameters(self):
         for model in self._config.bls_composing_models:
-            self._search_parameters[model.model_name()] = SearchParameters(
+            self._composing_search_parameters[model.model_name()] = SearchParameters(
                 self._config,
                 model.parameters(),
                 model.model_config_parameters(),
+                is_composing_model=True,
             )
diff --git a/model_analyzer/config/generate/search_parameters.py b/model_analyzer/config/generate/search_parameters.py
index 41986f410..9c2acab3d 100755
--- a/model_analyzer/config/generate/search_parameters.py
+++ b/model_analyzer/config/generate/search_parameters.py
@@ -46,12 +46,14 @@ def __init__(
         parameters: Dict[str, Any] = {},
         model_config_parameters: Dict[str, Any] = {},
         is_bls_model: bool = False,
+        is_composing_model: bool = False,
     ):
         self._config = config
         self._parameters = parameters
         self._model_config_parameters = model_config_parameters
         self._search_parameters: Dict[str, SearchParameter] = {}
         self._is_bls_model = is_bls_model
+        self._is_composing_model = is_composing_model
 
         self._populate_search_parameters()
 
@@ -123,7 +125,7 @@ def _populate_search_parameters(self) -> None:
     def _populate_parameters(self) -> None:
         self._populate_batch_sizes()
 
-        if not self._is_bls_model:
+        if not self._is_composing_model:
             self._populate_concurrency()
             # TODO: Populate request rate - TMA-1903
 
diff --git a/tests/test_search_parameters.py b/tests/test_search_parameters.py
index 80f0541a3..0ff4375b1 100755
--- a/tests/test_search_parameters.py
+++ b/tests/test_search_parameters.py
@@ -482,10 +482,11 @@ def test_search_parameter_creation_bls_default(self):
 
         analyzer = Analyzer(config, MagicMock(), MagicMock(), MagicMock())
         analyzer._populate_search_parameters()
+        analyzer._populate_composing_search_parameters()
 
         # ADD_SUB
         # =====================================================================
-        # The top level model of a BLS can only search instance count
+        # The top level model of a BLS does not search max batch size (always 1)
 
         # max_batch_size
         max_batch_size = analyzer._search_parameters["add_sub"].get_parameter(
@@ -497,7 +498,14 @@ def test_search_parameter_creation_bls_default(self):
         concurrency = analyzer._search_parameters["add_sub"].get_parameter(
             "concurrency"
         )
-        self.assertIsNone(concurrency)
+        self.assertEqual(ParameterUsage.RUNTIME, concurrency.usage)
+        self.assertEqual(ParameterCategory.EXPONENTIAL, concurrency.category)
+        self.assertEqual(
+            log2(default.DEFAULT_RUN_CONFIG_MIN_CONCURRENCY), concurrency.min_range
+        )
+        self.assertEqual(
+            log2(default.DEFAULT_RUN_CONFIG_MAX_CONCURRENCY), concurrency.max_range
+        )
 
         # instance_group
         instance_group = analyzer._search_parameters["add_sub"].get_parameter(
@@ -514,10 +522,10 @@ def test_search_parameter_creation_bls_default(self):
 
         # ADD/SUB (composing models)
         # =====================================================================
-        # The top level model of a BLS can only search instance count
+        # Composing models do not search concurrency
 
         # max_batch_size
-        max_batch_size = analyzer._search_parameters["add"].get_parameter(
+        max_batch_size = analyzer._composing_search_parameters["add"].get_parameter(
             "max_batch_size"
         )
         self.assertEqual(ParameterUsage.MODEL, max_batch_size.usage)
@@ -532,18 +540,13 @@ def test_search_parameter_creation_bls_default(self):
         )
 
         # concurrency
-        concurrency = analyzer._search_parameters["sub"].get_parameter("concurrency")
-        self.assertEqual(ParameterUsage.RUNTIME, concurrency.usage)
-        self.assertEqual(ParameterCategory.EXPONENTIAL, concurrency.category)
-        self.assertEqual(
-            log2(default.DEFAULT_RUN_CONFIG_MIN_CONCURRENCY), concurrency.min_range
-        )
-        self.assertEqual(
-            log2(default.DEFAULT_RUN_CONFIG_MAX_CONCURRENCY), concurrency.max_range
+        concurrency = analyzer._composing_search_parameters["sub"].get_parameter(
+            "concurrency"
         )
+        self.assertIsNone(concurrency)
 
         # instance_group
-        instance_group = analyzer._search_parameters["add"].get_parameter(
+        instance_group = analyzer._composing_search_parameters["sub"].get_parameter(
             "instance_group"
         )
         self.assertEqual(ParameterUsage.MODEL, instance_group.usage)