diff --git a/qiskit_experiments/base_experiment.py b/qiskit_experiments/base_experiment.py
index a78b64b240..929d78774b 100644
--- a/qiskit_experiments/base_experiment.py
+++ b/qiskit_experiments/base_experiment.py
@@ -77,9 +77,6 @@ def __init__(self, qubits: Iterable[int], experiment_type: Optional[str] = None)
         self._run_options = self._default_run_options()
         self._analysis_options = self._default_analysis_options()
 
-        # Set initial layout from qubits
-        self._transpile_options.initial_layout = list(self._physical_qubits)
-
     def run(
         self,
         backend: Backend,
@@ -125,7 +122,9 @@ def run(
         run_opts = run_opts.__dict__
 
         # Generate and transpile circuits
-        circuits = transpile(self.circuits(backend), backend, **self.transpile_options.__dict__)
+        transpile_opts = self.transpile_options.__dict__
+        transpile_opts["initial_layout"] = list(self._physical_qubits)
+        circuits = transpile(self.circuits(backend), backend, **transpile_opts)
         self._postprocess_transpiled_circuits(circuits, backend, **run_options)
 
         if isinstance(backend, LegacyBackend):
diff --git a/qiskit_experiments/composite/composite_experiment.py b/qiskit_experiments/composite/composite_experiment.py
index 91e21792c2..ba054ba25d 100644
--- a/qiskit_experiments/composite/composite_experiment.py
+++ b/qiskit_experiments/composite/composite_experiment.py
@@ -14,6 +14,7 @@
 """
 
 from abc import abstractmethod
+import warnings
 
 from qiskit_experiments.base_experiment import BaseExperiment
 from .composite_experiment_data import CompositeExperimentData
@@ -63,6 +64,17 @@ def _add_job_metadata(self, experiment_data, job, **run_options):
         # Add sub-experiment options
         for i in range(self.num_experiments):
             sub_exp = self.component_experiment(i)
+
+            # Run and transpile options are always overridden
+            if (
+                sub_exp.run_options != sub_exp._default_run_options()
+                or sub_exp.transpile_options != sub_exp._default_transpile_options()
+            ):
+
+                warnings.warn(
+                    "Sub-experiment run and transpile options"
+                    " are overridden by composite experiment options."
+                )
             sub_data = experiment_data.component_experiment_data(i)
             sub_exp._add_job_metadata(sub_data, job, **run_options)
 
diff --git a/test/analysis/test_curve_fit.py b/test/analysis/test_curve_fit.py
index 79345a5640..ef9da8ac78 100644
--- a/test/analysis/test_curve_fit.py
+++ b/test/analysis/test_curve_fit.py
@@ -15,6 +15,8 @@
 
 from typing import List
 
+from test.fake_experiment import FakeExperiment
+
 import numpy as np
 from qiskit.test import QiskitTestCase
 from qiskit.qobj.utils import MeasLevel
@@ -22,20 +24,9 @@
 from qiskit_experiments import ExperimentData
 from qiskit_experiments.analysis import CurveAnalysis, SeriesDef, fit_function
 from qiskit_experiments.analysis.data_processing import probability
-from qiskit_experiments.base_experiment import BaseExperiment
 from qiskit_experiments.exceptions import AnalysisError
 
 
-class FakeExperiment(BaseExperiment):
-    """A fake experiment class."""
-
-    def __init__(self):
-        super().__init__(qubits=(0,), experiment_type="fake_experiment")
-
-    def circuits(self, backend=None):
-        return []
-
-
 def simulate_output_data(func, xvals, param_dict, **metadata):
     """Generate arbitrary fit data."""
     __shots = 100000
diff --git a/test/data_processing/__init__.py b/test/data_processing/__init__.py
index e69de29bb2..784328ee92 100644
--- a/test/data_processing/__init__.py
+++ b/test/data_processing/__init__.py
@@ -0,0 +1,14 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2021.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""Data processing tests."""
+from .base_data_processor_test import BaseDataProcessorTest
diff --git a/test/data_processing/fake_experiment.py b/test/data_processing/base_data_processor_test.py
similarity index 72%
rename from test/data_processing/fake_experiment.py
rename to test/data_processing/base_data_processor_test.py
index d925c8d68e..d41c72e3fe 100644
--- a/test/data_processing/fake_experiment.py
+++ b/test/data_processing/base_data_processor_test.py
@@ -10,24 +10,10 @@
 # copyright notice, and modified files need to carry a notice indicating
 # that they have been altered from the originals.
 
-"""A FakeExperiment for data processor testing."""
+"""Base class for data processor tests."""
 
 from qiskit.test import QiskitTestCase
 from qiskit.qobj.common import QobjExperimentHeader
-from qiskit_experiments.base_experiment import BaseExperiment
-
-
-class FakeExperiment(BaseExperiment):
-    """Fake experiment class for testing."""
-
-    def __init__(self):
-        """Initialise the fake experiment."""
-        self._type = None
-        super().__init__((0,), "fake_test_experiment")
-
-    def circuits(self, backend=None):
-        """Fake circuits."""
-        return []
 
 
 class BaseDataProcessorTest(QiskitTestCase):
diff --git a/test/data_processing/test_data_processing.py b/test/data_processing/test_data_processing.py
index 70b4126d77..f756977a6f 100644
--- a/test/data_processing/test_data_processing.py
+++ b/test/data_processing/test_data_processing.py
@@ -14,7 +14,8 @@
 
 # pylint: disable=unbalanced-tuple-unpacking
 
-from test.data_processing.fake_experiment import FakeExperiment, BaseDataProcessorTest
+from test.fake_experiment import FakeExperiment
+
 import numpy as np
 from qiskit.result.models import ExperimentResultData, ExperimentResult
 from qiskit.result import Result
@@ -31,6 +32,8 @@
     MinMaxNormalize,
 )
 
+from . import BaseDataProcessorTest
+
 
 class DataProcessorTest(BaseDataProcessorTest):
     """Class to test DataProcessor."""
diff --git a/test/data_processing/test_nodes.py b/test/data_processing/test_nodes.py
index faaa9e9d1b..e01dba7b4d 100644
--- a/test/data_processing/test_nodes.py
+++ b/test/data_processing/test_nodes.py
@@ -14,7 +14,7 @@
 
 # pylint: disable=unbalanced-tuple-unpacking
 
-from test.data_processing.fake_experiment import FakeExperiment, BaseDataProcessorTest
+from test.fake_experiment import FakeExperiment
 
 from typing import Any, List
 import numpy as np
@@ -26,6 +26,8 @@
 from qiskit_experiments.data_processing.nodes import SVD, AverageData, MinMaxNormalize
 from qiskit_experiments.data_processing.data_processor import DataProcessor
 
+from . import BaseDataProcessorTest
+
 
 class TestAveraging(QiskitTestCase):
     """Test the averaging nodes."""
diff --git a/test/fake_backend.py b/test/fake_backend.py
new file mode 100644
index 0000000000..44ecd400f2
--- /dev/null
+++ b/test/fake_backend.py
@@ -0,0 +1,58 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2021.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""Fake backend class for tests."""
+from qiskit.providers.backend import BackendV1
+from qiskit.providers.models import QasmBackendConfiguration
+from qiskit.providers.options import Options
+
+from qiskit.result import Result
+
+from qiskit_experiments.test.mock_job import MockJob
+
+
+class FakeBackend(BackendV1):
+    """
+    Fake backend for test purposes only.
+    """
+
+    def __init__(self):
+        configuration = QasmBackendConfiguration(
+            backend_name="dummy_backend",
+            backend_version="0",
+            n_qubits=int(1e6),
+            basis_gates=["barrier", "x", "delay", "measure"],
+            gates=[],
+            local=True,
+            simulator=True,
+            conditional=False,
+            open_pulse=False,
+            memory=False,
+            max_shots=int(1e6),
+            coupling_map=None,
+        )
+        super().__init__(configuration)
+
+    @classmethod
+    def _default_options(cls):
+        return Options()
+
+    def run(self, run_input, **options):
+        result = {
+            "backend_name": "Dummmy backend",
+            "backend_version": "0",
+            "qobj_id": 0,
+            "job_id": 0,
+            "success": True,
+            "results": [],
+        }
+        return MockJob(backend=self, result=Result.from_dict(result))
diff --git a/test/fake_experiment.py b/test/fake_experiment.py
new file mode 100644
index 0000000000..93a9395f83
--- /dev/null
+++ b/test/fake_experiment.py
@@ -0,0 +1,46 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2021.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""A FakeExperiment for testing."""
+
+from qiskit.providers.options import Options
+
+from qiskit_experiments.base_experiment import BaseExperiment
+from qiskit_experiments.base_analysis import BaseAnalysis
+
+
+class FakeAnalysis(BaseAnalysis):
+    """
+    Dummy analysis class for test purposes only.
+    """
+
+    def _run_analysis(self, experiment_data, **options):
+        return [], None
+
+
+class FakeExperiment(BaseExperiment):
+    """Fake experiment class for testing."""
+
+    __analysis_class__ = FakeAnalysis
+
+    @classmethod
+    def _default_experiment_options(cls) -> Options:
+        return Options(dummyoption=None)
+
+    def __init__(self, qubit=0):
+        """Initialise the fake experiment."""
+        self._type = None
+        super().__init__((qubit,), "fake_test_experiment")
+
+    def circuits(self, backend=None):
+        """Fake circuits."""
+        return []
diff --git a/test/test_composite.py b/test/test_composite.py
new file mode 100644
index 0000000000..9b93fdce17
--- /dev/null
+++ b/test/test_composite.py
@@ -0,0 +1,55 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2021.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""Class to test composite experiments."""
+
+from test.fake_backend import FakeBackend
+from test.fake_experiment import FakeExperiment
+
+from qiskit.test import QiskitTestCase
+from qiskit.providers.options import Options
+
+from qiskit_experiments.composite.parallel_experiment import ParallelExperiment
+
+
+class TestComposite(QiskitTestCase):
+    """
+    Test composite experiment behavior.
+    """
+
+    def test_parallel_options(self):
+        """
+        Test parallel experiments overriding sub-experiment run and transpile options.
+        """
+
+        # These options will all be overridden
+        exp0 = FakeExperiment(0)
+        exp0.set_transpile_options(optimization_level=1)
+        exp2 = FakeExperiment(2)
+        exp2.set_experiment_options(dummyoption="test")
+        exp2.set_run_options(shots=2000)
+        exp2.set_transpile_options(optimization_level=1)
+        exp2.set_analysis_options(dummyoption="test")
+
+        par_exp = ParallelExperiment([exp0, exp2])
+
+        with self.assertWarnsRegex(
+            Warning,
+            "Sub-experiment run and transpile options"
+            " are overridden by composite experiment options.",
+        ):
+            self.assertEqual(par_exp.experiment_options, Options())
+            self.assertEqual(par_exp.run_options, Options(meas_level=2))
+            self.assertEqual(par_exp.transpile_options, Options(optimization_level=0))
+            self.assertEqual(par_exp.analysis_options, Options())
+
+            par_exp.run(FakeBackend())