diff --git a/lisp/ox.el b/lisp/ox.el
index 3f243a4fe..0d82913e6 100644
--- a/lisp/ox.el
+++ b/lisp/ox.el
@@ -2628,15 +2628,12 @@ from tree."
 			;; If headline is archived but tree below has
 			;; to be skipped, remove contents.
 			(org-element-set-contents data)
-		      ;; Move into secondary string, if any.
-		      (let ((sec-prop
-			     (cdr (assq type
-					org-element-secondary-value-alist))))
-			(when sec-prop
-			  (mapc walk-data
-				(org-element-property sec-prop data))))
 		      ;; Move into recursive objects/elements.
-		      (mapc walk-data (org-element-contents data)))))))))
+		      (mapc walk-data (org-element-contents data)))
+		    ;; Move into secondary string, if any.
+		    (dolist (p (cdr (assq type
+					  org-element-secondary-value-alist)))
+		      (mapc walk-data (org-element-property p data)))))))))
     ;; If a select tag is active, also ignore the section before the
     ;; first headline, if any.
     (when selected
diff --git a/testing/lisp/test-ox.el b/testing/lisp/test-ox.el
index e6b631a04..96cc5d4dd 100644
--- a/testing/lisp/test-ox.el
+++ b/testing/lisp/test-ox.el
@@ -591,11 +591,11 @@ Paragraph"
 			   nil nil nil '(:with-properties ("B"))))))
   ;; Statistics cookies.
   (should
-   (equal ""
+   (equal "* Stats"
 	  (let (org-export-filter-body-functions
 		org-export-filter-final-output-functions)
 	    (org-trim
-	     (org-test-with-temp-text "[0/0]"
+	     (org-test-with-temp-text "* Stats [0/0]"
 	       (org-export-as (org-test-default-backend)
 			      nil nil nil '(:with-statistics-cookies nil)))))))
   ;; Tables.