diff --git a/src/core/evaluator.js b/src/core/evaluator.js
index e75fdff9ca7f0..5384db2b47afb 100644
--- a/src/core/evaluator.js
+++ b/src/core/evaluator.js
@@ -4558,9 +4558,22 @@ class PartialEvaluator {
       throw new FormatError("invalid font name");
     }
 
-    let fontFile, subtype, length1, length2, length3;
+    let fontFile, fontFileN, subtype, length1, length2, length3;
     try {
-      fontFile = descriptor.get("FontFile", "FontFile2", "FontFile3");
+      fontFile = descriptor.get("FontFile");
+      if (fontFile) {
+        fontFileN = 1;
+      } else {
+        fontFile = descriptor.get("FontFile2");
+        if (fontFile) {
+          fontFileN = 2;
+        } else {
+          fontFile = descriptor.get("FontFile3");
+          if (fontFile) {
+            fontFileN = 3;
+          }
+        }
+      }
 
       if (fontFile) {
         if (!(fontFile instanceof BaseStream)) {
@@ -4662,6 +4675,7 @@ class PartialEvaluator {
       name: fontName.name,
       subtype,
       file: fontFile,
+      fontFileN,
       length1,
       length2,
       length3,
diff --git a/src/core/fonts.js b/src/core/fonts.js
index a155ac70283ab..ab92840fd2530 100644
--- a/src/core/fonts.js
+++ b/src/core/fonts.js
@@ -2642,7 +2642,8 @@ class Font {
     if (!isTrueType) {
       // OpenType font (skip composite fonts with non-default glyph mapping).
       if (
-        (header.version === "OTTO" && !properties.composite) ||
+        (header.version === "OTTO" &&
+          (!properties.composite || properties.fontFileN === 3)) ||
         !tables.head ||
         !tables.hhea ||
         !tables.maxp ||
diff --git a/test/pdfs/.gitignore b/test/pdfs/.gitignore
index 6080768c93f9e..89ce5d446ca79 100644
--- a/test/pdfs/.gitignore
+++ b/test/pdfs/.gitignore
@@ -768,3 +768,4 @@
 !issue20513.pdf
 !issue20516.pdf
 !issue20489.pdf
+!Embedded_font.pdf
diff --git a/test/pdfs/Embedded_font.pdf b/test/pdfs/Embedded_font.pdf
new file mode 100644
index 0000000000000..448715103bb47
Binary files /dev/null and b/test/pdfs/Embedded_font.pdf differ
diff --git a/test/test_manifest.json b/test/test_manifest.json
index 860497c72ebc9..06dfaef6720a6 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -13131,5 +13131,12 @@
     "rounds": 1,
     "link": true,
     "type": "eq"
+  },
+  {
+    "id": "Embedded_font.pdf",
+    "file": "pdfs/Embedded_font.pdf",
+    "md5": "5625dc05630ca728f45b02baf11dc540",
+    "rounds": 1,
+    "type": "eq"
   }
 ]