diff --git a/.coveragerc b/.coveragerc
index b4e940b7..703ae66d 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -1,5 +1,3 @@
-# Coverage isn't really compatible with subprocesses so results are unreliable
-
 [paths]
 source =
 	src
@@ -8,9 +6,11 @@ source =
 [run]
 branch = true
 parallel = true
+concurrency =
+	thread
+	multiprocessing
 source =
 	src/ocrmypdf
-	tests
 omit =
 	tests/spoof/*
 
diff --git a/tests/conftest.py b/tests/conftest.py
index 075e004e..90e9057d 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -229,13 +229,21 @@ def run_ocrmypdf(input_file, output_file, *args, env=None, universal_newlines=Tr
     "Run ocrmypdf and let caller deal with results"
 
     if env is None:
-        env = os.environ
+        env = os.environ.copy()
 
     p_args = (
         OCRMYPDF
         + [str(arg) for arg in args if arg is not None]
         + [str(input_file), str(output_file)]
     )
+
+    # Tell subprocess where to find coverage.py configuration
+    # This has no effect except when coverage is running
+    # Details: https://coverage.readthedocs.io/en/coverage-5.0/subprocess.html
+    coverage_rc = Path(__file__).parent.parent / '.coveragerc'
+    assert coverage_rc.exists()
+    env['COVERAGE_PROCESS_START'] = os.fspath(coverage_rc)
+
     p = run(
         p_args, stdout=PIPE, stderr=PIPE, universal_newlines=universal_newlines, env=env
     )