diff --git a/EXPERIMENTAL/org-e-ascii.el b/EXPERIMENTAL/org-e-ascii.el
index 487ed6eff..c93009196 100644
--- a/EXPERIMENTAL/org-e-ascii.el
+++ b/EXPERIMENTAL/org-e-ascii.el
@@ -54,7 +54,7 @@
 (declare-function org-export-get-footnote-number "org-export" (footnote info))
 (declare-function org-export-get-headline-number "org-export" (headline info))
 (declare-function org-export-get-ordinal "org-export"
-		  (element info &optional types within-section predicate))
+		  (element info &optional types predicate))
 (declare-function org-export-get-parent-headline "org-export" (blob info))
 (declare-function org-export-get-relative-level "org-export" (headline info))
 (declare-function org-export-handle-code
@@ -642,7 +642,7 @@ keyword."
       ;; src-block with either a caption or a name.
       (let ((reference
 	     (org-export-get-ordinal
-	      element info nil nil
+	      element info nil
 	      (lambda (el) (or (org-element-property :caption el)
 			  (org-element-property :name el)))))
 	    (title-fmt (org-e-ascii--translate
diff --git a/contrib/lisp/org-export.el b/contrib/lisp/org-export.el
index a946ebc87..22a76998d 100644
--- a/contrib/lisp/org-export.el
+++ b/contrib/lisp/org-export.el
@@ -2865,8 +2865,7 @@ INFO is a plist holding export options."
 ;; `org-export-get-ordinal' associates a sequence number to any object
 ;; or element.
 
-(defun org-export-get-ordinal
-  (element info &optional types within-section predicate)
+(defun org-export-get-ordinal (element info &optional types predicate)
   "Return ordinal number of an element or object.
 
 ELEMENT is the element or object considered.  INFO is the plist
@@ -2876,15 +2875,11 @@ Optional argument TYPES, when non-nil, is a list of element or
 object types, as symbols, that should also be counted in.
 Otherwise, only provided element's type is considered.
 
-When optional argument WITHIN-SECTION is non-nil, narrow counting
-to the section containing ELEMENT.
-
 Optional argument PREDICATE is a function returning a non-nil
 value if the current element or object should be counted in.  It
-accepts one argument: the element or object being considered.
-This argument allows to count only a certain type of objects,
-like inline images, which are a subset of links (in that case,
-`org-export-inline-image-p' might be an useful predicate).
+accepts two arguments: the element or object being considered and
+the plist used as a communication channel.  This allows to count
+only a certain type of objects (i.e. inline images).
 
 Return value is a list of numbers if ELEMENT is an headline or an
 item.  It is nil for keywords.  It represents the footnote number
@@ -2920,24 +2915,15 @@ objects of the same type."
       ((footnote definition footnote-reference)
        (org-export-get-footnote-number element info))
       (otherwise
-       (let ((counter 0)
-	     ;; Determine if search should apply to current section,
-	     ;; in which case it should be retrieved first, or to full
-	     ;; parse tree.  As a special case, an element or object
-	     ;; without a parent headline will also trigger a full
-	     ;; search, notwithstanding WITHIN-SECTION value.
-	     (data
-	      (if (not within-section) (plist-get info :parse-tree)
-		(or (org-export-get-parent-headline element info)
-		    (plist-get info :parse-tree)))))
+       (let ((counter 0))
 	 ;; Increment counter until ELEMENT is found again.
 	 (org-element-map
-	  data (or types (org-element-type element))
+	  (plist-get info :parse-tree) (or types (org-element-type element))
 	  (lambda (el)
 	    (cond
 	     ((equal element el) (1+ counter))
 	     ((not predicate) (incf counter) nil)
-	     ((funcall predicate el) (incf counter) nil)))
+	     ((funcall predicate el info) (incf counter) nil)))
 	  info 'first-match))))))