diff --git a/Documentation/kbuild/makefiles.rst b/Documentation/kbuild/makefiles.rst
index 68ed20ef37dd..78aa51a6fcd4 100644
--- a/Documentation/kbuild/makefiles.rst
+++ b/Documentation/kbuild/makefiles.rst
@@ -765,7 +765,8 @@ Files matching the patterns "*.[oas]", "*.ko", plus some additional files
 generated by kbuild are deleted all over the kernel src tree when
 "make clean" is executed.
 
-Additional files can be specified in kbuild makefiles by use of $(clean-files).
+Additional files or directories can be specified in kbuild makefiles by use of
+$(clean-files).
 
 	Example::
 
@@ -776,17 +777,8 @@ When executing "make clean", the file "crc32table.h" will be deleted.
 Kbuild will assume files to be in the same relative directory as the
 Makefile, except if prefixed with $(objtree).
 
-To delete a directory hierarchy use:
-
-	Example::
-
-		#scripts/package/Makefile
-		clean-dirs := $(objtree)/debian/
-
-This will delete the directory debian in the toplevel directory, including all
-subdirectories.
-
-To exclude certain files from make clean, use the $(no-clean-files) variable.
+To exclude certain files or directories from make clean, use the
+$(no-clean-files) variable.
 
 Usually kbuild descends down in subdirectories due to "obj-* := dir/",
 but in the architecture makefiles where the kbuild infrastructure
diff --git a/Makefile b/Makefile
index e88d4fcd5e87..ec2a6b85a0fa 100644
--- a/Makefile
+++ b/Makefile
@@ -1448,13 +1448,11 @@ distclean: mrproper
 
 # Packaging of the kernel to various formats
 # ---------------------------------------------------------------------------
-package-dir	:= scripts/package
 
 %src-pkg: FORCE
-	$(Q)$(MAKE) $(build)=$(package-dir) $@
+	$(Q)$(MAKE) -f $(srctree)/scripts/Makefile.package $@
 %pkg: include/config/kernel.release FORCE
-	$(Q)$(MAKE) $(build)=$(package-dir) $@
-
+	$(Q)$(MAKE) -f $(srctree)/scripts/Makefile.package $@
 
 # Brief documentation of the typical targets used
 # ---------------------------------------------------------------------------
@@ -1526,7 +1524,7 @@ help:
 	@echo '  or  "cd tools; make help"'
 	@echo  ''
 	@echo  'Kernel packaging:'
-	@$(MAKE) $(build)=$(package-dir) help
+	@$(MAKE) -f $(srctree)/scripts/Makefile.package help
 	@echo  ''
 	@echo  'Documentation targets:'
 	@$(MAKE) -f $(srctree)/Documentation/Makefile dochelp
diff --git a/scripts/Makefile.clean b/scripts/Makefile.clean
index 0b80e3207b20..798e8717c1d9 100644
--- a/scripts/Makefile.clean
+++ b/scripts/Makefile.clean
@@ -52,26 +52,14 @@ __clean-files   := $(wildcard                                               \
 		   $(addprefix $(obj)/, $(filter-out $(objtree)/%, $(__clean-files))) \
 		   $(filter $(objtree)/%, $(__clean-files)))
 
-# same as clean-files
-
-__clean-dirs    := $(wildcard                                               \
-		   $(addprefix $(obj)/, $(filter-out $(objtree)/%, $(clean-dirs)))    \
-		   $(filter $(objtree)/%, $(clean-dirs)))
-
 # ==========================================================================
 
 quiet_cmd_clean    = CLEAN   $(obj)
-      cmd_clean    = rm -f $(__clean-files)
-quiet_cmd_cleandir = CLEAN   $(__clean-dirs)
-      cmd_cleandir = rm -rf $(__clean-dirs)
-
+      cmd_clean    = rm -rf $(__clean-files)
 
 __clean: $(subdir-ymn)
 ifneq ($(strip $(__clean-files)),)
 	+$(call cmd,clean)
-endif
-ifneq ($(strip $(__clean-dirs)),)
-	+$(call cmd,cleandir)
 endif
 	@:
 
diff --git a/scripts/package/Makefile b/scripts/Makefile.package
similarity index 99%
rename from scripts/package/Makefile
rename to scripts/Makefile.package
index 407189d9942a..56eadcc48d46 100644
--- a/scripts/package/Makefile
+++ b/scripts/Makefile.package
@@ -1,6 +1,7 @@
 # SPDX-License-Identifier: GPL-2.0-only
 # Makefile for the different targets used to generate full packages of a kernel
-# It uses the generic clean infrastructure of kbuild
+
+include $(srctree)/scripts/Kbuild.include
 
 # RPM target
 # ---------------------------------------------------------------------------
@@ -154,3 +155,5 @@ help:
 	@echo '  perf-targz-src-pkg  - Build $(perf-tar).tar.gz source tarball'
 	@echo '  perf-tarbz2-src-pkg - Build $(perf-tar).tar.bz2 source tarball'
 	@echo '  perf-tarxz-src-pkg  - Build $(perf-tar).tar.xz source tarball'
+
+.PHONY: $(PHONY)
diff --git a/scripts/kconfig/Makefile b/scripts/kconfig/Makefile
index 7656e1137b6b..bed7a5a2fbe9 100644
--- a/scripts/kconfig/Makefile
+++ b/scripts/kconfig/Makefile
@@ -114,7 +114,7 @@ testconfig: $(obj)/conf
 	$(PYTHON3) -B -m pytest $(srctree)/$(src)/tests \
 	-o cache_dir=$(abspath $(obj)/tests/.cache) \
 	$(if $(findstring 1,$(KBUILD_VERBOSE)),--capture=no)
-clean-dirs += tests/.cache
+clean-files += tests/.cache
 
 # Help text used by make help
 help:
diff --git a/usr/include/Makefile b/usr/include/Makefile
index 1fb6abe29b2f..05c71ef42f51 100644
--- a/usr/include/Makefile
+++ b/usr/include/Makefile
@@ -115,6 +115,4 @@ header-test-y += $(filter-out $(header-test-), \
 			$(patsubst $(obj)/%,%, $(wildcard \
 			$(addprefix $(obj)/, *.h */*.h */*/*.h */*/*/*.h))))
 
-# For GNU Make <= 4.2.1, $(wildcard $(obj)/*/) matches to not only directories
-# but also regular files. Use $(filter %/, ...) just in case.
-clean-dirs += $(patsubst $(obj)/%/,%,$(filter %/, $(wildcard $(obj)/*/)))
+clean-files += $(filter-out Makefile, $(notdir $(wildcard $(obj)/*)))
