diff --git a/git-rebase.sh b/git-rebase.sh
index 60b70f3..a299bcc 100755
--- a/git-rebase.sh
+++ b/git-rebase.sh
@@ -518,7 +518,7 @@
 esac
 
 # If the branch to rebase is given, that is the branch we will rebase
-# $branch_name -- branch being rebased, or HEAD (already detached)
+# $branch_name -- branch/commit being rebased, or HEAD (already detached)
 # $orig_head -- commit object name of tip of the branch before rebasing
 # $head_name -- refs/heads/<that-branch> or "detached HEAD"
 switch_to=
@@ -528,15 +528,18 @@
 	branch_name="$1"
 	switch_to="$1"
 
-	if git show-ref --verify --quiet -- "refs/heads/$1" &&
-	   orig_head=$(git rev-parse -q --verify "refs/heads/$1")
+	# Is it a local branch?
+	if git show-ref --verify --quiet -- "refs/heads/$branch_name" &&
+	   orig_head=$(git rev-parse -q --verify "refs/heads/$branch_name")
 	then
-		head_name="refs/heads/$1"
-	elif orig_head=$(git rev-parse -q --verify "$1")
+		head_name="refs/heads/$branch_name"
+	# If not is it a valid ref (branch or commit)?
+	elif orig_head=$(git rev-parse -q --verify "$branch_name")
 	then
 		head_name="detached HEAD"
+
 	else
-		die "$(eval_gettext "fatal: no such branch: \$branch_name")"
+		die "$(eval_gettext "fatal: no such branch/commit: \$branch_name")"
 	fi
 	;;
 0)
@@ -547,7 +550,7 @@
 		branch_name=$(expr "z$branch_name" : 'zrefs/heads/\(.*\)')
 	else
 		head_name="detached HEAD"
-		branch_name=HEAD ;# detached
+		branch_name=HEAD
 	fi
 	orig_head=$(git rev-parse --verify HEAD) || exit
 	;;