diff --git i/admin/unidata/emoji-zwj.awk w/admin/unidata/emoji-zwj.awk
index 3d605d5d64..331095d56f 100644
--- i/admin/unidata/emoji-zwj.awk
+++ w/admin/unidata/emoji-zwj.awk
@@ -69,6 +69,7 @@ END {
      # emoji sequences.  We have code in font.c:font_range that will
      # try to display them with the emoji font anyway.
 
+     trigger_codepoints[0] = "20E3"
      trigger_codepoints[1] = "261D"
      trigger_codepoints[2] = "26F9"
      trigger_codepoints[3] = "270C"
diff --git i/src/font.c w/src/font.c
index 7e0219181c..265bec6ce5 100644
--- i/src/font.c
+++ w/src/font.c
@@ -3937,6 +3937,14 @@ codepoint_is_emoji_eligible (int ch)
   return false;
 }
 
+static bool
+codepoint_is_combining_lookup_eligible (int ch)
+{
+  if ((0x20D0 <= ch && ch <= 0x20FF) || ch == 0x308)
+    return true;
+  return false;
+}
+
 /* Check how many characters after character/byte position POS/POS_BYTE
    (at most to *LIMIT) can be displayed by the same font in the window W.
    FACE, if non-NULL, is the face selected for the character at POS.
@@ -3996,6 +4004,13 @@ font_range (ptrdiff_t pos, ptrdiff_t pos_byte, ptrdiff_t *limit,
 	    val = AREF (val, 0);
 	  font_object = font_for_char (face, XFIXNAT (val), pos, string);
 	}
+    } else if (codepoint_is_combining_lookup_eligible (ch))
+  /* If the triggering codepoint is a combining character, use the
+     font of that character rather than the font of the base
+     character, since that increases the chances of composition
+     working.  */
+    {
+      font_object = font_for_char (face, ch, pos, string);
     }
 
   while (pos < *limit)