diff --git a/admin/unidata/emoji-zwj.awk b/admin/unidata/emoji-zwj.awk
index 7d2ff6cb900..f13f796bcac 100644
--- a/admin/unidata/emoji-zwj.awk
+++ b/admin/unidata/emoji-zwj.awk
@@ -106,7 +106,8 @@ END {
 
      for (elt in ch)
     {
-        printf("(#x%s .\n,(eval-when-compile (regexp-opt\n'(\n%s\n))))\n", elt, vec[elt])
+        entries = sprintf("%s\n\"\\N{U+%s}\\N{U+FE0E}\"\n\"\\N{U+%s}\\N{U+FE0F}\"", vec[elt], elt, elt)
+        printf("(#x%s .\n,(eval-when-compile (regexp-opt\n'(\n%s\n))))\n", elt, entries)
     }
      print "))"
      print "  (set-char-table-range composition-function-table"
diff --git a/lisp/composite.el b/lisp/composite.el
index fb8b76114f4..9710c3c371b 100644
--- a/lisp/composite.el
+++ b/lisp/composite.el
@@ -861,7 +861,7 @@ and the second is a glyph for a variation selector."
 ;; handled in font_range, we end up choosing the Emoji presentation
 ;; rather than the Text presentation.
 (let ((elt '([".." 1 compose-gstring-for-variation-glyph])))
-  (set-char-table-range composition-function-table '(#xFE00 . #xFE0E) elt)
+  (set-char-table-range composition-function-table '(#xFE00 . #xFE0D) elt)
   (set-char-table-range composition-function-table '(#xE0100 . #xE01EF) elt))
 
 (defun auto-compose-chars (func from to font-object string direction)