diff --git a/Lib/test/test_embed.py b/Lib/test/test_embed.py
index c7f45b59ac..033bdbbf03 100644
--- a/Lib/test/test_embed.py
+++ b/Lib/test/test_embed.py
@@ -51,7 +51,7 @@ class EmbeddingTests(unittest.TestCase):
         if p.returncode != 0 and support.verbose:
             print(f"--- {cmd} failed ---")
             print(f"stdout:\n{out}")
-            print(f"stderr:\n{out}")
+            print(f"stderr:\n{err}")
             print(f"------")
 
         self.assertEqual(p.returncode, 0,
@@ -83,7 +83,7 @@ class EmbeddingTests(unittest.TestCase):
         for line in out.splitlines():
             if line == "--- Pass {} ---".format(numloops):
                 self.assertEqual(len(current_run), 0)
-                if support.verbose:
+                if support.verbose > 1:
                     print(line)
                 numloops += 1
                 continue
@@ -96,7 +96,7 @@ class EmbeddingTests(unittest.TestCase):
             # Parse the line from the loop.  The first line is the main
             # interpreter and the 3 afterward are subinterpreters.
             interp = Interp(*match.groups())
-            if support.verbose:
+            if support.verbose > 1:
                 print(interp)
             self.assertTrue(interp.interp)
             self.assertTrue(interp.tstate)
@@ -190,12 +190,23 @@ class EmbeddingTests(unittest.TestCase):
 
     def test_pre_initialization_api(self):
         """
-        Checks the few parts of the C-API that work before the runtine
+        Checks some key parts of the C-API that need to work before the runtine
         is initialized (via Py_Initialize()).
         """
         env = dict(os.environ, PYTHONPATH=os.pathsep.join(sys.path))
         out, err = self.run_embedded_interpreter("pre_initialization_api", env=env)
-        self.assertEqual(out, '')
+        # Allow debugging output on "out"
+        self.assertEqual(err, '')
+
+    def test_pre_initialization_sys_options(self):
+        """
+        Checks that sys.warnoptions and sys._xoptions can be set before the
+        runtime is initialized (otherwise they won't be effective).
+        """
+        env = dict(os.environ, PYTHONPATH=os.pathsep.join(sys.path))
+        out, err = self.run_embedded_interpreter(
+                        "pre_initialization_sys_options", env=env)
+        # Allow debugging output on "out"
         self.assertEqual(err, '')
 
     def test_bpo20891(self):
diff --git a/Programs/_testembed.c b/Programs/_testembed.c
index b3d7aa442d..c7116d9b93 100644
--- a/Programs/_testembed.c
+++ b/Programs/_testembed.c
@@ -130,23 +130,53 @@ static int test_forced_io_encoding(void)
  * Test parts of the C-API that work before initialization
  *********************************************************/
 
+/* The pre-initialization tests tend to break by segfaulting, so explicitly
+ * flushed progress messages make the broken API easier to find when they fail.
+ */
+#define _Py_EMBED_PREINIT_CHECK(msg) \
+    do {printf(msg); fflush(stdout);} while (0);
+
 static int test_pre_initialization_api(void)
 {
     /* Leading "./" ensures getpath.c can still find the standard library */
+    _Py_EMBED_PREINIT_CHECK("Checking Py_DecodeLocale\n");
     wchar_t *program = Py_DecodeLocale("./spam", NULL);
     if (program == NULL) {
         fprintf(stderr, "Fatal error: cannot decode program name\n");
         return 1;
     }
+    _Py_EMBED_PREINIT_CHECK("Checking Py_SetProgramName\n");
     Py_SetProgramName(program);
 
+    _Py_EMBED_PREINIT_CHECK("Initializing interpreter\n");
     Py_Initialize();
+    _Py_EMBED_PREINIT_CHECK("Finalizing interpreter\n");
     Py_Finalize();
 
+    _Py_EMBED_PREINIT_CHECK("Freeing memory allocated by Py_DecodeLocale\n");
     PyMem_RawFree(program);
     return 0;
 }
 
+
+/* bpo-33042: Ensure embedding apps can predefine sys module options */
+static int test_pre_initialization_sys_options(void)
+{
+    _Py_EMBED_PREINIT_CHECK("Checking Py_SysAddWarnOption\n");
+    PySys_AddWarnOption(L"default");
+    _Py_EMBED_PREINIT_CHECK("Checking Py_SysAddXOption\n");
+    PySys_AddXOption(L"not_an_option=1");
+
+    _Py_EMBED_PREINIT_CHECK("Initializing interpreter\n");
+    Py_Initialize();
+    _Py_EMBED_PREINIT_CHECK("Finalizing interpreter\n");
+    Py_Finalize();
+
+    return 0;
+}
+
+
+/* bpo-20891: Avoid race condition when initialising the GIL */
 static void bpo20891_thread(void *lockp)
 {
     PyThread_type_lock lock = *((PyThread_type_lock*)lockp);
@@ -217,6 +247,7 @@ static struct TestCase TestCases[] = {
     { "forced_io_encoding", test_forced_io_encoding },
     { "repeated_init_and_subinterpreters", test_repeated_init_and_subinterpreters },
     { "pre_initialization_api", test_pre_initialization_api },
+    { "pre_initialization_sys_options", test_pre_initialization_sys_options },
     { "bpo20891", test_bpo20891 },
     { NULL, NULL }
 };
@@ -232,13 +263,13 @@ int main(int argc, char *argv[])
 
     /* No match found, or no test name provided, so display usage */
     printf("Python " PY_VERSION " _testembed executable for embedded interpreter tests\n"
-           "Normally executed via 'EmbeddingTests' in Lib/test/test_capi.py\n\n"
+           "Normally executed via 'EmbeddingTests' in Lib/test/test_embed.py\n\n"
            "Usage: %s TESTNAME\n\nAll available tests:\n", argv[0]);
     for (struct TestCase *tc = TestCases; tc && tc->name; tc++) {
         printf("  %s\n", tc->name);
     }
 
-    /* Non-zero exit code will cause test_capi.py tests to fail.
+    /* Non-zero exit code will cause test_embed.py tests to fail.
        This is intentional. */
     return -1;
 }