diff --git a/Lib/compileall.py b/Lib/compileall.py
index 8cfde5b..1831ad7 100644
--- a/Lib/compileall.py
+++ b/Lib/compileall.py
@@ -46,7 +46,7 @@
 
 def compile_dir(dir, maxlevels=None, ddir=None, force=False,
                 rx=None, quiet=0, legacy=False, optimize=-1, workers=1,
-                invalidation_mode=None, stripdir=None,
+                invalidation_mode=None, *, stripdir=None,
                 prependdir=None, limit_sl_dest=None):
     """Byte-compile all modules in the given directory tree.
 
@@ -72,6 +72,13 @@
                    the defined path
     """
     ProcessPoolExecutor = None
+    if ddir is not None and (stripdir is not None or prependdir is not None):
+        raise ValueError(("Destination dir (ddir) cannot be used "
+                          "in combination with stripdir or prependdir"))
+    if ddir is not None:
+        stripdir = dir
+        prependdir = ddir
+        ddir = None
     if workers < 0:
         raise ValueError('workers must be greater or equal to 0')
     if workers != 1:
@@ -111,7 +118,7 @@
 
 def compile_file(fullname, ddir=None, force=False, rx=None, quiet=0,
                  legacy=False, optimize=-1,
-                 invalidation_mode=None, stripdir=None, prependdir=None,
+                 invalidation_mode=None, *, stripdir=None, prependdir=None,
                  limit_sl_dest=None):
     """Byte-compile one file.
 
diff --git a/Lib/test/test_compileall.py b/Lib/test/test_compileall.py
index 2ebcb42..cb59fd7 100644
--- a/Lib/test/test_compileall.py
+++ b/Lib/test/test_compileall.py
@@ -212,6 +212,47 @@
         compileall.compile_dir(self.directory, quiet=True, maxlevels=depth)
         self.assertTrue(os.path.isfile(pyc_filename))
 
+    def _test_ddir_only(self, *, ddir, parallel=True):
+        """Recursive compile_dir ddir must contain package paths; bpo39769."""
+        fullpath = ["test", "foo"]
+        path = self.directory
+        mods = []
+        for subdir in fullpath:
+            path = os.path.join(path, subdir)
+            os.mkdir(path)
+            script_helper.make_script(path, "__init__", "")
+            mods.append(script_helper.make_script(path, "mod",
+                                                  "def fn(): 1/0\nfn()\n"))
+        compileall.compile_dir(
+                self.directory, quiet=True, ddir=ddir,
+                workers=2 if parallel else 1)
+        self.assertTrue(mods)
+        for mod in mods:
+            self.assertTrue(mod.startswith(self.directory), mod)
+            modcode = importlib.util.cache_from_source(mod)
+            modpath = mod[len(self.directory+os.sep):]
+            _, _, err = script_helper.assert_python_failure(modcode)
+            expected_in = os.path.join(ddir, modpath)
+            mod_code_obj = test.test_importlib.util.get_code_from_pyc(modcode)
+            self.assertEqual(mod_code_obj.co_filename, expected_in)
+            self.assertIn(f'"{expected_in}"', os.fsdecode(err))
+
+    def test_ddir_only_one_worker(self):
+        """Recursive compile_dir ddir= contains package paths; bpo39769."""
+        return self._test_ddir_only(ddir="<a prefix>", parallel=False)
+
+    def test_ddir_multiple_workers(self):
+        """Recursive compile_dir ddir= contains package paths; bpo39769."""
+        return self._test_ddir_only(ddir="<a prefix>", parallel=True)
+
+    def test_ddir_empty_only_one_worker(self):
+        """Recursive compile_dir ddir='' contains package paths; bpo39769."""
+        return self._test_ddir_only(ddir="", parallel=False)
+
+    def test_ddir_empty_multiple_workers(self):
+        """Recursive compile_dir ddir='' contains package paths; bpo39769."""
+        return self._test_ddir_only(ddir="", parallel=True)
+
     def test_strip_only(self):
         fullpath = ["test", "build", "real", "path"]
         path = os.path.join(self.directory, *fullpath)
diff --git a/Lib/test/test_importlib/util.py b/Lib/test/test_importlib/util.py
index 5aaf277..de6e0b0 100644
--- a/Lib/test/test_importlib/util.py
+++ b/Lib/test/test_importlib/util.py
@@ -7,6 +7,7 @@
 from importlib import machinery, util, invalidate_caches
 from importlib.abc import ResourceReader
 import io
+import marshal
 import os
 import os.path
 from pathlib import Path, PurePath
@@ -118,6 +119,16 @@
     return '{}.{}'.format(parent, name), path
 
 
+def get_code_from_pyc(pyc_path):
+    """Reads a pyc file and returns the unmarshalled code object within.
+
+    No header validation is performed.
+    """
+    with open(pyc_path, 'rb') as pyc_f:
+        pyc_f.seek(16)
+        return marshal.load(pyc_f)
+
+
 @contextlib.contextmanager
 def uncache(*names):
     """Uncache a module from sys.modules.