diff --git a/scripts/setlocalversion b/scripts/setlocalversion
index 4f1d3eb795e9..38b96c6797f4 100755
--- a/scripts/setlocalversion
+++ b/scripts/setlocalversion
@@ -57,21 +57,37 @@ scm_version()
 		return
 	fi
 
-	# If a localversion*' file and the corresponding annotated tag exist,
-	# use it. This is the case in linux-next.
+	# mainline kernel:  6.2.0-rc5  ->  v6.2-rc5
+	# stable kernel:    6.1.7      ->  v6.1.7
+	version_tag=v$(echo "${KERNELVERSION}" | sed -E 's/^([0-9]+\.[0-9]+)\.0(.*)$/\1\2/')
+
+	# If a localversion* file exists, and the corresponding
+	# annotated tag exists and is an ancestor of HEAD, use
+	# it. This is the case in linux-next.
 	tag=${file_localversion#-}
-	tag=$(git describe --exact-match --match=$tag $tag 2>/dev/null)
+	desc=
+	if [ -n "${tag}" ]; then
+		desc=$(git describe --match=$tag 2>/dev/null)
+	fi
+
+	# Otherwise, if a localversion* file exists, and the tag
+	# obtained by appending it to the tag derived from
+	# KERNELVERSION exists and is an ancestor of HEAD, use
+	# it. This is e.g. the case in linux-rt.
+	if [ -z "${desc}" ] && [ -n "${file_localversion}" ]; then
+		tag="${version_tag}${file_localversion}"
+		desc=$(git describe --match=$tag 2>/dev/null)
+	fi
 
 	# Otherwise, default to the annotated tag derived from KERNELVERSION.
-	#   mainline kernel:  6.2.0-rc5  ->  v6.2-rc5
-	#   stable kernel:    6.1.7      ->  v6.1.7
-	if [ -z "${tag}" ]; then
-		tag=v$(echo "${KERNELVERSION}" | sed -E 's/^([0-9]+\.[0-9]+)\.0(.*)$/\1\2/')
+	if [ -z "${desc}" ]; then
+		tag="${version_tag}"
+		desc=$(git describe --match=$tag 2>/dev/null)
 	fi
 
 	# If we are at the tagged commit, we ignore it because the version is
 	# well-defined.
-	if [ -z "$(git describe --exact-match --match=$tag 2>/dev/null)" ]; then
+	if [ "${tag}" != "${desc}" ]; then
 
 		# If only the short version is requested, don't bother
 		# running further git commands
@@ -81,8 +97,8 @@ scm_version()
 		fi
 		# If we are past the tagged commit, we pretty print it.
 		# (like 6.1.0-14595-g292a089d78d3)
-		if atag="$(git describe --match=$tag 2>/dev/null)"; then
-			echo "$atag" | awk -F- '{printf("-%05d", $(NF-1))}'
+		if [ -n "${desc}" ]; then
+			echo "${desc}" | awk -F- '{printf("-%05d", $(NF-1))}'
 		fi
 
 		# Add -g and exactly 12 hex chars.