diff --git a/continuous_integration/run_tests.sh b/continuous_integration/run_tests.sh
index f26f0fdc..078bc89a 100755
--- a/continuous_integration/run_tests.sh
+++ b/continuous_integration/run_tests.sh
@@ -18,4 +18,8 @@ fi
 # launching the tests:
 python -m threadpoolctl -i numpy scipy.linalg tests._openmp_test_helper.openmp_helpers_inner
 
+# Introspect API scope:
+PYTHONPATH=. python tests/empirical_scope_observation.py blas
+PYTHONPATH=. python tests/empirical_scope_observation.py openmp
+
 pytest -vlrxXs -W error -k "$TESTS" --junitxml=test_result.xml --cov=threadpoolctl --cov-report xml
diff --git a/dev-requirements.txt b/dev-requirements.txt
index 04901b66..d98aa93a 100644
--- a/dev-requirements.txt
+++ b/dev-requirements.txt
@@ -1,5 +1,6 @@
 flit
 coverage
+psutil
 pytest
 pytest-cov
 cython
diff --git a/tests/empirical_scope_observation.py b/tests/empirical_scope_observation.py
new file mode 100644
index 00000000..8624820a
--- /dev/null
+++ b/tests/empirical_scope_observation.py
@@ -0,0 +1,123 @@
+"""
+Run this script to empirically determine if OpenMP and BLAS limiting API set
+the size of a shared process-wide thread pool or a per-thread limit.
+"""
+
+import sys
+from concurrent.futures import ThreadPoolExecutor
+from os import cpu_count
+from pprint import pprint
+from threading import Thread
+from typing import Callable
+
+import threadpoolctl
+import psutil
+
+
+def start_counting_threads() -> Callable[[], int]:
+    num_threads = 0
+    stop = False
+
+    def in_thread():
+        nonlocal num_threads, stop
+        process = psutil.Process()
+        while not stop:
+            num_threads = max(num_threads, process.num_threads())
+
+    thread = Thread(target=in_thread)
+    thread.start()
+
+    def finish():
+        nonlocal stop, num_threads
+        stop = True
+        thread.join()
+        return num_threads
+
+    return finish
+
+
+def set_limits():
+    threadpoolctl.threadpool_limits(2)
+    print("== Library info ==")
+    pprint(threadpoolctl.threadpool_info())
+    print()
+
+
+def blas(num_python_threads):
+    try:
+        import numpy as np
+    except ImportError:
+        print("BLAS not available")
+        return False
+
+    set_limits()
+    A = np.ones((10_000_000,))
+
+    def blas_math(_):
+        A.dot(A)
+
+    with ThreadPoolExecutor(num_python_threads) as pool:
+        for _ in pool.map(blas_math, range(400)):
+            pass
+
+    return True
+
+
+def openmp(num_python_threads):
+    try:
+        from tests._openmp_test_helper.openmp_helpers_inner import (
+            check_openmp_num_threads,
+        )
+    except ImportError:
+        print("OpenMP not available")
+        return False
+
+    set_limits()
+
+    def run_openmp(_):
+        check_openmp_num_threads(1000)
+
+    with ThreadPoolExecutor(num_python_threads) as pool:
+        for _ in pool.map(run_openmp, range(400)):
+            pass
+
+    return True
+
+
+def run(which: str) -> None:
+    if which == "blas":
+        func = blas
+    else:
+        func = openmp
+
+    num_python_threads = 10 * cpu_count()
+    count_threads = start_counting_threads()
+    if not func(num_python_threads):
+        count_threads()
+        return
+    max_num_threads = count_threads()
+
+    # We're creating os.cpu_count() * 10 Python threads, and asking for 2
+    # native threads. If number is close to number of Python threads, we'll
+    # assume process-wide shared thread pool. If the number is close to double
+    # the number of Python threads, we'll assume a thread pool per thread.
+    if max_num_threads < num_python_threads * 1.25:
+        scope = "process-wide shared thread pool"
+    elif max_num_threads > num_python_threads * 1.75:
+        scope = "thread pool per thread"
+    else:
+        scope = "not sure"
+
+    print(f"== Observed behavior: {which} ==")
+    print("Maximum number of observed threads:", max_num_threads)
+    print("Presumed API scope:", scope)
+    print()
+
+
+if __name__ == "__main__":
+    if sys.argv[1] == "openmp":
+        run("openmp")
+    elif sys.argv[1] == "blas":
+        run("blas")
+    else:
+        raise SystemExit("Bad argument")