diff --git a/src/core/evaluator.js b/src/core/evaluator.js
index 51c0c511c..ab8fc66dc 100644
--- a/src/core/evaluator.js
+++ b/src/core/evaluator.js
@@ -2115,7 +2115,7 @@ class PartialEvaluator {
 
       if (
         font.isType3Font &&
-        textState.fontSize <= 1 &&
+        (textState.fontSize <= 1 || font.isCharBBox) &&
         !isArrayEqual(textState.fontMatrix, FONT_IDENTITY_MATRIX)
       ) {
         const glyphHeight = font.bbox[3] - font.bbox[1];
@@ -3815,7 +3815,7 @@ class PartialEvaluator {
       firstChar,
       lastChar,
       toUnicode,
-      bbox: descriptor.getArray("FontBBox"),
+      bbox: descriptor.getArray("FontBBox") || dict.getArray("FontBBox"),
       ascent: descriptor.get("Ascent"),
       descent: descriptor.get("Descent"),
       xHeight: descriptor.get("XHeight"),
@@ -3962,6 +3962,9 @@ class TranslatedFont {
     const fontResources = this.dict.get("Resources") || resources;
     const charProcOperatorList = Object.create(null);
 
+    const isEmptyBBox =
+      !translatedFont.bbox || isArrayEqual(translatedFont.bbox, [0, 0, 0, 0]);
+
     for (const key of charProcs.getKeys()) {
       loadCharProcsPromise = loadCharProcsPromise.then(() => {
         const glyphStream = charProcs.get(key);
@@ -3981,7 +3984,7 @@ class TranslatedFont {
             //   colour-related parameters) in the graphics state;
             //   any use of such operators shall be ignored."
             if (operatorList.fnArray[0] === OPS.setCharWidthAndBounds) {
-              this._removeType3ColorOperators(operatorList);
+              this._removeType3ColorOperators(operatorList, isEmptyBBox);
             }
             charProcOperatorList[key] = operatorList.getIR();
 
@@ -3996,8 +3999,12 @@ class TranslatedFont {
           });
       });
     }
-    this.type3Loaded = loadCharProcsPromise.then(function () {
+    this.type3Loaded = loadCharProcsPromise.then(() => {
       translatedFont.charProcOperatorList = charProcOperatorList;
+      if (this._bbox) {
+        translatedFont.isCharBBox = true;
+        translatedFont.bbox = this._bbox;
+      }
     });
     return this.type3Loaded;
   }
@@ -4005,7 +4012,7 @@ class TranslatedFont {
   /**
    * @private
    */
-  _removeType3ColorOperators(operatorList) {
+  _removeType3ColorOperators(operatorList, isEmptyBBox = false) {
     if (
       typeof PDFJSDev === "undefined" ||
       PDFJSDev.test("!PRODUCTION || TESTING")
@@ -4015,6 +4022,17 @@ class TranslatedFont {
         "Type3 glyph shall start with the d1 operator."
       );
     }
+    if (isEmptyBBox) {
+      if (!this._bbox) {
+        this._bbox = [Infinity, Infinity, -Infinity, -Infinity];
+      }
+      const charBBox = Util.normalizeRect(operatorList.argsArray[0].slice(2));
+
+      this._bbox[0] = Math.min(this._bbox[0], charBBox[0]);
+      this._bbox[1] = Math.min(this._bbox[1], charBBox[1]);
+      this._bbox[2] = Math.max(this._bbox[2], charBBox[2]);
+      this._bbox[3] = Math.max(this._bbox[3], charBBox[3]);
+    }
     let i = 1,
       ii = operatorList.length;
     while (i < ii) {
diff --git a/test/pdfs/.gitignore b/test/pdfs/.gitignore
index d42280b85..30b829844 100644
--- a/test/pdfs/.gitignore
+++ b/test/pdfs/.gitignore
@@ -437,6 +437,7 @@
 !quadpoints.pdf
 !transparent.pdf
 !xobject-image.pdf
+!issue6605.pdf
 !ccitt_EndOfBlock_false.pdf
 !issue9972-1.pdf
 !issue9972-2.pdf
diff --git a/test/pdfs/issue6605.pdf b/test/pdfs/issue6605.pdf
new file mode 100644
index 000000000..529f9ccd6
Binary files /dev/null and b/test/pdfs/issue6605.pdf differ
diff --git a/test/test_manifest.json b/test/test_manifest.json
index a4afb11b4..f089bfd05 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -4935,6 +4935,12 @@
        "type": "eq",
        "annotations": true
     },
+    {  "id": "issue6605",
+       "file": "pdfs/issue6605.pdf",
+       "md5": "67158a9c6d0e966ece55f7c433e18cc5",
+       "rounds": 1,
+       "type": "text"
+    },
     {  "id": "annotation-choice-widget-forms",
        "file": "pdfs/annotation-choice-widget.pdf",
        "md5": "7dfb0d743a0da0f4a71b209ab43b0be5",