diff --git a/lisp/org-element.el b/lisp/org-element.el
index da17de6b6..6b4dd29a0 100644
--- a/lisp/org-element.el
+++ b/lisp/org-element.el
@@ -2495,6 +2495,7 @@ LIMIT bounds the search.
 Return value is a cons cell whose CAR is `entity' or
 `latex-fragment' and CDR is beginning position."
   (save-excursion
+    (unless (bolp) (backward-char))
     (let ((matchers
 	   (remove "begin" (plist-get org-format-latex-options :matchers)))
 	  ;; ENTITY-RE matches both LaTeX commands and Org entities.
@@ -3189,6 +3190,7 @@ LIMIT bounds the search.
 Return value is a cons cell whose CAR is either `subscript' or
 `superscript' and CDR is beginning position."
   (save-excursion
+    (unless (bolp) (backward-char))
     (when (re-search-forward org-match-substring-regexp limit t)
       (cons (if (string= (match-string 2) "_") 'subscript 'superscript)
 	    (match-beginning 2)))))
@@ -3984,8 +3986,14 @@ type, as a symbol.
 
 OBJECTS is the previous candidates alist."
   ;; Filter out any object found but not belonging to RESTRICTION.
-  (setq objects (org-remove-if-not (lambda (obj) (memq (car obj) restriction))
-				   objects))
+  (setq objects
+	(org-remove-if-not
+	 (lambda (obj)
+	   (let ((type (car obj)))
+	     (memq (or (cdr (assq type org-element-object-successor-alist))
+		       type)
+		   restriction)))
+	 objects))
   (let (next-candidates types-to-search)
     ;; If no previous result, search every object type in RESTRICTION.
     ;; Otherwise, keep potential candidates (old objects located after
diff --git a/testing/lisp/test-org-element.el b/testing/lisp/test-org-element.el
index b3b7e4c1e..3c4ef81b7 100644
--- a/testing/lisp/test-org-element.el
+++ b/testing/lisp/test-org-element.el
@@ -1093,7 +1093,13 @@ e^{i\\pi}+1=0
     (should
      (org-test-with-temp-text "\\[a\\]"
        (org-element-map
-	(org-element-parse-buffer) 'latex-fragment 'identity)))))
+	(org-element-parse-buffer) 'latex-fragment 'identity)))
+    ;; Test fragment at the beginning of an item.
+    (should
+     (eq 'latex-fragment
+	 (org-test-with-temp-text "- $x$"
+	   (progn (search-forward "$")
+		  (org-element-type (org-element-context))))))))
 
 
 ;;;; Line Break
@@ -1576,7 +1582,19 @@ Outside list"
   ;; With braces.
   (should
    (org-test-with-temp-text "a_{b}"
-     (org-element-map (org-element-parse-buffer) 'subscript 'identity))))
+     (org-element-map (org-element-parse-buffer) 'subscript 'identity)))
+  ;; At the beginning of an item.
+  (should
+   (eq 'subscript
+       (org-test-with-temp-text "- _b"
+	 (progn (search-forward "_")
+		(org-element-type (org-element-context))))))
+  ;; Multiple subscripts in a paragraph.
+  (should
+   (= 2
+      (org-test-with-temp-text "a_b and c_d"
+	(length
+	 (org-element-map (org-element-parse-buffer) 'subscript 'identity))))))
 
 
 ;;;; Superscript
@@ -1590,7 +1608,20 @@ Outside list"
   ;; With braces.
   (should
    (org-test-with-temp-text "a^{b}"
-     (org-element-map (org-element-parse-buffer) 'superscript 'identity))))
+     (org-element-map (org-element-parse-buffer) 'superscript 'identity)))
+  ;; At the beginning of an item.
+  (should
+   (eq 'superscript
+       (org-test-with-temp-text "- ^b"
+	 (progn (search-forward "^")
+		(org-element-type (org-element-context))))))
+  ;; Multiple superscript in a paragraph.
+  (should
+   (= 2
+      (org-test-with-temp-text "a^b and c^d"
+	(length
+	 (org-element-map
+	  (org-element-parse-buffer) 'superscript 'identity))))))
 
 
 ;;;; Table