diff --git a/lisp/org.el b/lisp/org.el
index bb83eb7c6..9283d3644 100644
--- a/lisp/org.el
+++ b/lisp/org.el
@@ -6065,11 +6065,17 @@ by a #."
 (defvar org-target-link-regexp nil
   "Regular expression matching radio targets in plain text.")
 (make-variable-buffer-local 'org-target-link-regexp)
-(defvar org-target-regexp "<<\\([^<>\n\r]+\\)>>"
+
+(defconst org-target-regexp (let ((border "[^<>\n\r \t]"))
+			      (format "<<\\(%s\\|%s[^<>\n\r]*%s\\)>>"
+				      border border border))
   "Regular expression matching a link target.")
-(defvar org-radio-target-regexp "<<<\\([^<>\n\r]+\\)>>>"
+
+(defconst org-radio-target-regexp (format "<%s>" org-target-regexp)
   "Regular expression matching a radio target.")
-(defvar org-any-target-regexp "<<<?\\([^<>\n\r]+\\)>>>?" ; FIXME, not exact, would match <<<aaa>>  as a radio target.
+
+(defconst org-any-target-regexp
+  (format "%s\\|%s" org-radio-target-regexp org-target-regexp)
   "Regular expression matching any target.")
 
 (defun org-activate-target-links (limit)
diff --git a/testing/lisp/test-org-element.el b/testing/lisp/test-org-element.el
index def1659cc..d6e38ff85 100644
--- a/testing/lisp/test-org-element.el
+++ b/testing/lisp/test-org-element.el
@@ -1699,6 +1699,15 @@ Outside list"
   (should
    (eq 'radio-target
        (org-test-with-temp-text "<<<\\alpha radio>>>"
+	 (org-element-type (org-element-context)))))
+  ;; Radio targets cannot begin or end with white space.
+  (should-not
+   (eq 'radio-target
+       (org-test-with-temp-text "<<< radio>>>"
+	 (org-element-type (org-element-context)))))
+  (should-not
+   (eq 'radio-target
+       (org-test-with-temp-text "<<<radio >>>"
 	 (org-element-type (org-element-context))))))