diff --git a/lisp/org.el b/lisp/org.el
index 987e8f1d3..6218a3a81 100755
--- a/lisp/org.el
+++ b/lisp/org.el
@@ -10708,7 +10708,8 @@ link in a property drawer line."
 	 ((memq type '(comment comment-block keyword node-property))
 	  (cond ((org-in-regexp org-any-link-re)
 		 (org-open-link-from-string (match-string-no-properties 0)))
-		((or (org-at-timestamp-p t) (org-at-date-range-p t))
+		((or (org-in-regexp org-ts-regexp-both nil t)
+		     (org-in-regexp org-tsr-regexp-both nil t))
 		 (org-follow-timestamp-link))
 		(t (user-error "No link found"))))
 	 ;; On a headline or an inlinetask, but not on a timestamp,
@@ -10736,13 +10737,12 @@ link in a property drawer line."
 	       (>= (point) (org-element-property :begin value))
 	       (<= (point) (org-element-property :end value)))
 	  (org-follow-timestamp-link))
-	 ;; Do nothing on white spaces after an object, unless point
-	 ;; is right after it.
-	 ((> (point)
-	     (save-excursion
-	       (goto-char (org-element-property :end context))
-	       (skip-chars-backward " \t")
-	       (point)))
+	 ;; Do nothing on white spaces after an object.
+	 ((>= (point)
+	      (save-excursion
+		(goto-char (org-element-property :end context))
+		(skip-chars-backward " \t")
+		(point)))
 	  (user-error "No link found"))
 	 ((eq type 'timestamp) (org-follow-timestamp-link))
 	 ;; On tags within a headline or an inlinetask.
@@ -21349,13 +21349,13 @@ object (e.g., within a comment).  In these case, you need to use
 	  (org-element-lineage context '(table-row table-cell) t))
       (org-table-justify-field-maybe)
       (call-interactively #'org-table-next-row))
-     ;; On a link or a timestamp, call `org-open-line' if
+     ;; On a link or a timestamp, call `org-open-at-point' if
      ;; `org-return-follows-link' allows it.  Tolerate fuzzy
-     ;; locations, e.g., in a comment, as `org-open-line'.
+     ;; locations, e.g., in a comment, as `org-open-at-point'.
      ((and org-return-follows-link
-	   (or (org-at-timestamp-p t)
-	       (org-at-date-range-p t)
-	       (org-in-regexp org-any-link-re)))
+	   (or (org-in-regexp org-ts-regexp-both nil t)
+	       (org-in-regexp org-tsr-regexp-both nil  t)
+	       (org-in-regexp org-any-link-re nil t)))
       (call-interactively #'org-open-at-point))
      ;; Insert newline in heading, but preserve tags.
      ((and (not (bolp))
diff --git a/testing/lisp/test-org.el b/testing/lisp/test-org.el
index 861134d76..dc8f2fb16 100644
--- a/testing/lisp/test-org.el
+++ b/testing/lisp/test-org.el
@@ -982,6 +982,12 @@
 	   (org-link-search-must-match-exact-headline nil))
        (org-return))
      (org-looking-at-p "<<target>>")))
+  (should-not
+   (org-test-with-temp-text "Link [[target]]<point> <<target>>"
+     (let ((org-return-follows-link t)
+	   (org-link-search-must-match-exact-headline nil))
+       (org-return))
+     (org-looking-at-p "<<target>>")))
   ;; When `org-return-follows-link' is non-nil, tolerate links and
   ;; timestamps in comments, node properties, etc.
   (should
@@ -990,6 +996,16 @@
 	   (org-link-search-must-match-exact-headline nil))
        (org-return))
      (org-looking-at-p "<<target>>")))
+  (should-not
+   (org-test-with-temp-text "# Comment [[target<point>]]\n <<target>>"
+     (let ((org-return-follows-link nil)) (org-return))
+     (org-looking-at-p "<<target>>")))
+  (should-not
+   (org-test-with-temp-text "# Comment [[target]]<point>\n <<target>>"
+     (let ((org-return-follows-link t)
+	   (org-link-search-must-match-exact-headline nil))
+       (org-return))
+     (org-looking-at-p "<<target>>")))
   ;; However, do not open link when point is in a table.
   (should
    (org-test-with-temp-text "| [[target<point>]] |\n| between |\n| <<target>> |"
@@ -1606,7 +1622,7 @@
 #+BEGIN_SRC emacs-lisp
 \(+ 1 1)                  (ref:sc)
 #+END_SRC
-\[[(sc)]]<point>"
+\[[(sc)<point>]]"
      (org-open-at-point)
      (looking-at "(ref:sc)")))
   ;; Find coderef even with alternate label format.
@@ -1615,7 +1631,7 @@
 #+BEGIN_SRC emacs-lisp -l \"{ref:%s}\"
 \(+ 1 1)                  {ref:sc}
 #+END_SRC
-\[[(sc)]]<point>"
+\[[(sc)<point>]]"
      (org-open-at-point)
      (looking-at "{ref:sc}"))))
 
@@ -1625,13 +1641,13 @@
   "Test custom ID links specifications."
   (should
    (org-test-with-temp-text
-       "* H1\n:PROPERTIES:\n:CUSTOM_ID: custom\n:END:\n* H2\n[[#custom]]<point>"
+       "* H1\n:PROPERTIES:\n:CUSTOM_ID: custom\n:END:\n* H2\n[[#custom<point>]]"
      (org-open-at-point)
      (org-looking-at-p "\\* H1")))
   ;; Throw an error on false positives.
   (should-error
    (org-test-with-temp-text
-       "* H1\n:DRAWER:\n:CUSTOM_ID: custom\n:END:\n* H2\n[[#custom]]<point>"
+       "* H1\n:DRAWER:\n:CUSTOM_ID: custom\n:END:\n* H2\n[[#custom<point>]]"
      (org-open-at-point)
      (org-looking-at-p "\\* H1"))))
 
@@ -1705,8 +1721,7 @@
      (looking-at "\\* COMMENT Test")))
   ;; Correctly un-hexify fuzzy links.
   (should
-   (org-test-with-temp-text "* With space\n[[*With%20space][With space]]"
-     (goto-char (point-max))
+   (org-test-with-temp-text "* With space\n[[*With%20space][With space<point>]]"
      (org-open-at-point)
      (bobp))))