diff --git a/src/fonts.js b/src/fonts.js
index 928c63b0a..48dc7c941 100644
--- a/src/fonts.js
+++ b/src/fonts.js
@@ -4171,12 +4171,16 @@ var Font = (function FontClosure() {
       }
 
       var cidEncoding = properties.cidEncoding;
-      if (cidEncoding && cidEncoding.indexOf('Identity-') !== 0) {
+      if (!cidEncoding) {
+        return;
+      }
+      if (cidEncoding.indexOf('Identity-') !== 0) {
         // input is already Unicode for non-Identity CMap encodings.
-        // However, Unicode-to-CID conversion is needed
-        // regardless of the CMap encoding. So we can't reset
-        // unicodeToCID.
         this.cidToUnicode = [];
+      } else {
+        // We don't have to do reverse conversions if the string is
+        // already CID.
+        this.unicodeToCID = [];
       }
     },
 
diff --git a/test/pdfs/.gitignore b/test/pdfs/.gitignore
index dd9335f3a..9e0c0ffd5 100644
--- a/test/pdfs/.gitignore
+++ b/test/pdfs/.gitignore
@@ -40,6 +40,7 @@
 !mixedfonts.pdf
 !shading_extend.pdf
 !noembed-identity.pdf
+!noembed-identity-2.pdf
 !noembed-jis7.pdf
 !noembed-eucjp.pdf
 !noembed-sjis.pdf
diff --git a/test/pdfs/noembed-identity-2.pdf b/test/pdfs/noembed-identity-2.pdf
new file mode 100644
index 000000000..5bc89bea6
Binary files /dev/null and b/test/pdfs/noembed-identity-2.pdf differ
diff --git a/test/test_manifest.json b/test/test_manifest.json
index 8fbe6531f..9a4f938ce 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -823,6 +823,12 @@
       "rounds": 1,
       "type": "eq"
     },
+    {  "id": "noembed-identity-2",
+      "file": "pdfs/noembed-identity-2.pdf",
+      "md5": "5549571a910814a9c53a1761b27fd028",
+      "rounds": 1,
+      "type": "eq"
+    },
     {  "id": "noembed-jis7",
       "file": "pdfs/noembed-jis7.pdf",
       "md5": "a0f6cf5a830f23d0c35994a6aaf92b3d",