diff --git a/src/core/fonts.js b/src/core/fonts.js
index 2c9ffa94e..ae9ced291 100644
--- a/src/core/fonts.js
+++ b/src/core/fonts.js
@@ -2377,7 +2377,10 @@ var Font = (function FontClosure() {
             charCodeToGlyphId[charCode] = glyphId;
           }
         });
-        if (dupFirstEntry) {
+        if (dupFirstEntry && (isCidToGidMapEmpty || !charCodeToGlyphId[0])) {
+          // We don't duplicate the first entry in the `charCodeToGlyphId` map
+          // if the font has a `CIDToGIDMap` which has already mapped the first
+          // entry to a non-zero `glyphId` (fixes issue7544.pdf).
           charCodeToGlyphId[0] = numGlyphs - 1;
         }
       } else {
diff --git a/test/pdfs/.gitignore b/test/pdfs/.gitignore
index 06486ca08..2852407f8 100644
--- a/test/pdfs/.gitignore
+++ b/test/pdfs/.gitignore
@@ -35,6 +35,7 @@
 !issue7439.pdf
 !issue7446.pdf
 !issue7492.pdf
+!issue7544.pdf
 !issue7598.pdf
 !filled-background.pdf
 !ArabicCIDTrueType.pdf
diff --git a/test/pdfs/issue7544.pdf b/test/pdfs/issue7544.pdf
new file mode 100644
index 000000000..8e030933a
Binary files /dev/null and b/test/pdfs/issue7544.pdf differ
diff --git a/test/test_manifest.json b/test/test_manifest.json
index 1d27162d4..866c3f540 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -1014,6 +1014,13 @@
        "rounds": 1,
        "type": "eq"
     },
+    {  "id": "issue7544",
+       "file": "pdfs/issue7544.pdf",
+       "md5": "87e3a9fc7d6a6c1bd5b53af6926ce48e",
+       "link": false,
+       "rounds": 1,
+       "type": "eq"
+    },
     {  "id": "protectip",
        "file": "pdfs/protectip.pdf",
        "md5": "676e7a7b8f96d04825361832b1838a93",