diff --git a/Makefile.pre.in b/Makefile.pre.in
index 83788a64038..798c53fa7c6 100644
--- a/Makefile.pre.in
+++ b/Makefile.pre.in
@@ -720,15 +720,13 @@ Makefile Modules/config.c: Makefile.pre \
 	@mv config.c Modules
 	@echo "The Makefile was updated, you may need to re-run make."
 
+.PHONY: regen-test-frozenmain
 regen-test-frozenmain: $(BUILDPYTHON)
 	# Regenerate Programs/test_frozenmain.h
 	# from Programs/test_frozenmain.py
 	# using Programs/freeze_test_frozenmain.py
 	$(RUNSHARED) ./$(BUILDPYTHON) Programs/freeze_test_frozenmain.py Programs/test_frozenmain.h
 
-Programs/test_frozenmain.h: Programs/freeze_test_frozenmain.py Programs/test_frozenmain.py
-	$(MAKE) regen-test-frozenmain
-
 Programs/_testembed: Programs/_testembed.o $(LIBRARY_DEPS)
 	$(LINKCC) $(PY_CORE_LDFLAGS) $(LINKFORSHARED) -o $@ Programs/_testembed.o $(BLDLIBRARY) $(LIBS) $(MODLIBS) $(SYSLIBS)
 
diff --git a/Programs/test_frozenmain.h b/Programs/test_frozenmain.h
index ac3dfd32c26..e680b80e7ae 100644
--- a/Programs/test_frozenmain.h
+++ b/Programs/test_frozenmain.h
@@ -25,6 +25,6 @@ unsigned char M_test_frozenmain[] = {
     169,0,114,7,0,0,0,114,7,0,0,0,250,18,116,101,
     115,116,95,102,114,111,122,101,110,109,97,105,110,46,112,121,
     218,8,60,109,111,100,117,108,101,62,1,0,0,0,115,16,
-    0,0,0,8,0,8,1,8,2,12,1,12,1,18,1,18,
+    0,0,0,8,3,8,1,8,2,12,1,12,1,18,1,18,
     1,22,1,243,0,0,0,0,
 };
diff --git a/Programs/test_frozenmain.py b/Programs/test_frozenmain.py
index aa79106df63..928b9ea816a 100644
--- a/Programs/test_frozenmain.py
+++ b/Programs/test_frozenmain.py
@@ -1,3 +1,6 @@
+# Script used to test Py_FrozenMain(): see test_embed.test_frozenmain().
+# Run "make regen-test-frozenmain" if you modify this test.
+
 import sys
 import _testinternalcapi