diff --git a/brp-python-bytecompile b/brp-python-bytecompile
index cbc5830..7e20608 100644
--- a/brp-python-bytecompile
+++ b/brp-python-bytecompile
@@ -26,12 +26,13 @@ fi
 
 # This function now implements Python byte-compilation in three different ways:
 # Python >= 3.4 and < 3.9 uses a new module compileall2 - https://github.com/fedora-python/compileall2
+# In Python >= 3.9, compileall2 was merged back to standard library (compileall) so we can use it directly again.
 # Python < 3.4 (inc. Python 2) uses compileall module from stdlib with some hacks
+
 # When we drop support for Python 2, we'd be able to use all compileall2 features like:
 # - -s and -p options to manipulate with a path baked into pyc files instead of $real_libdir
 # - removed useless $depth - both compileall and compileall2 are limited by sys.getrecursionlimit()
 # These changes will make this script much simpler
-# In Python >= 3.9, compileall2 was merged back to standard library (compileall) so we can use it directly again.
 function python_bytecompile()
 {
     local options=$1
@@ -41,45 +42,40 @@ function python_bytecompile()
     local depth=$5 # Not used for Python >= 3.4
     local real_libdir=$6 # Not used for Python >= 3.4
 
-	python_version=$($python_binary -c "import sys; sys.stdout.write('{0.major}{0.minor}'.format(sys.version_info))")
+    python_version=$($python_binary -c "import sys; sys.stdout.write('{0.major}{0.minor}'.format(sys.version_info))")
 
-	#
-	# Python 3.9 and higher
-	#
-	if [ "$python_version" -ge 39 ]; then
+    #
+    # Python 3.4 and higher
+    #
+    if [ "$python_version" -ge 34 ]; then
 
-		# For Python 3.9+, we compile all opt levels in one go: only
-		# when $options is empty.
-		if [ -n "$options" ]; then
-		    return
-		fi
+        # We compile all opt levels in one go: only when $options is empty.
+        if [ -n "$options" ]; then
+            return
+        fi
 
-		[ ! -z $exclude ] && exclude="-x '$exclude'"
-		# -q disables verbose output
-		# -f forces the process to overwrite existing compiled files
-		# -x excludes paths defined by regex
-		# -e excludes symbolic links pointing outside the build root
-		# -x and -e together implements the same functionality as the Filter class below
-		# -s strips $RPM_BUILD_ROOT from the path
-		# -p prepends the leading slash to the path to make it absolute
-		$python_binary -B -m compileall -o 0 -o 1 -q -f $exclude -s "$RPM_BUILD_ROOT" -p / --hardlink-dupes -e "$RPM_BUILD_ROOT" "$python_libdir"
+        if [ "$python_version" -ge 39 ]; then
+            # For Pyhon 3.9+, use the standard library
+            compileall_module=compileall
+        else
+            # For older Pythons, use compileall2
+            compileall_module=compileall2
+        fi
 
-	#
-	# Python 3.4 and higher
-	#
-	elif [ "$python_version" -ge 34 ]; then
+        [ ! -z $exclude ] && exclude="-x '$exclude'"
 
-		[ ! -z $exclude ] && exclude="-x '$exclude'"
-		# /usr/lib/rpm/redhat/ contains compileall2 Python module
-		# -q disables verbose output
-		# -f forces the process to overwrite existing compiled files
-		# -x excludes paths defined by regex
-		# -e excludes symbolic links pointing outside the build root
-		# -x and -e together implements the same functionality as the Filter class below
-		# -s strips $RPM_BUILD_ROOT from the path
-		# -p prepends the leading slash to the path to make it absolute
-		PYTHONPATH=/usr/lib/rpm/redhat/ $python_binary -B $options -m compileall2 -q -f $exclude -s "$RPM_BUILD_ROOT" -p / -e "$RPM_BUILD_ROOT" "$python_libdir"
-	else
+        # PYTHONPATH is needed for compileall2, but doesn't hurt for the stdlib
+        # -o 0 -o 1 are the optimization levels
+        # -q disables verbose output
+        # -f forces the process to overwrite existing compiled files
+        # -x excludes paths defined by regex
+        # -e excludes symbolic links pointing outside the build root
+        # -x and -e together implements the same functionality as the Filter class below
+        # -s strips $RPM_BUILD_ROOT from the path
+        # -p prepends the leading slash to the path to make it absolute
+        PYTHONPATH=/usr/lib/rpm/redhat/ $python_binary -B -m $compileall_module -o 0 -o 1 -q -f $exclude -s "$RPM_BUILD_ROOT" -p / --hardlink-dupes -e "$RPM_BUILD_ROOT" "$python_libdir"
+
+    else
 #
 # Python 3.3 and lower (incl. Python 2)
 #
@@ -138,7 +134,7 @@ do
 	fi
 
 	# Generate optimized (.pyo) byte-compiled files.
-	# N.B. For Python 3.9+, this call does nothing
+	# N.B. For Python 3.4+, this call does nothing
 	python_bytecompile "-O" "$python_binary" "" "$python_libdir" "$depth" "$real_libdir"
 	if [ $? -ne 0 -a 0$errors_terminate -ne 0 ]; then
 		# One or more of the files had a syntax error
diff --git a/macros.pybytecompile b/macros.pybytecompile
index 6c89c8b..9dabee0 100644
--- a/macros.pybytecompile
+++ b/macros.pybytecompile
@@ -28,7 +28,7 @@ py2_byte_compile () {\
 py3_byte_compile () {\
     python_binary="env PYTHONHASHSEED=0 %1"\
     bytecode_compilation_path="%2"\
-    PYTHONPATH="%{_rpmconfigdir}/redhat" $python_binary -s -B -m compileall2 -o 0 -o 1 -s $RPM_BUILD_ROOT -p / $bytecode_compilation_path \
+    PYTHONPATH="%{_rpmconfigdir}/redhat" $python_binary -s -B -m compileall2 -o 0 -o 1 -s $RPM_BUILD_ROOT -p / --hardlink-dupes $bytecode_compilation_path \
 }\
 \
 py39_byte_compile () {\
diff --git a/python-rpm-macros.spec b/python-rpm-macros.spec
index e39b07f..624a66e 100644
--- a/python-rpm-macros.spec
+++ b/python-rpm-macros.spec
@@ -143,7 +143,7 @@ install -m 755 brp-* %{buildroot}%{_rpmconfigdir}/redhat/
 %changelog
 * Thu Sep 09 2021 Petr Viktorin <pviktori@redhat.com> - 3.10-8
 - Use --hardlink-dupes in %%py_byte_compile and brp-python-bytecompile
-  (for Python 3.9+)
+  (for Python 3)
 - Resolves: rhbz#1977895
 
 * Fri Jul 23 2021 Fedora Release Engineering <releng@fedoraproject.org> - 3.9-7