diff --git a/src/core/fonts.js b/src/core/fonts.js
index 0f457bcb7..ece712180 100644
--- a/src/core/fonts.js
+++ b/src/core/fonts.js
@@ -3222,7 +3222,7 @@ var Font = (function FontClosure() {
        * Read the appropriate subtable from the cmap according to 9.6.6.4 from
        * PDF spec
        */
-      function readCmapTable(cmap, font, isSymbolicFont) {
+      function readCmapTable(cmap, font, isSymbolicFont, hasEncoding) {
         var segment;
         var start = (font.start ? font.start : 0) + cmap.offset;
         font.pos = start;
@@ -3253,7 +3253,7 @@ var Font = (function FontClosure() {
             // Continue the loop since there still may be a higher priority
             // table.
           } else if (platformId === 3 && encodingId === 1 &&
-                     (!isSymbolicFont || !potentialTable)) {
+                     ((!isSymbolicFont && hasEncoding) || !potentialTable)) {
             useTable = true;
             if (!isSymbolicFont) {
               canBreak = true;
@@ -4202,13 +4202,14 @@ var Font = (function FontClosure() {
       } else {
         // Most of the following logic in this code branch is based on the
         // 9.6.6.4 of the PDF spec.
-        var cmapTable = readCmapTable(tables.cmap, font, this.isSymbolicFont);
+        var hasEncoding =
+          properties.differences.length > 0 || !!properties.baseEncodingName;
+        var cmapTable =
+          readCmapTable(tables.cmap, font, this.isSymbolicFont, hasEncoding);
         var cmapPlatformId = cmapTable.platformId;
         var cmapEncodingId = cmapTable.encodingId;
         var cmapMappings = cmapTable.mappings;
         var cmapMappingsLength = cmapMappings.length;
-        var hasEncoding = properties.differences.length ||
-                          !!properties.baseEncodingName;
 
         // The spec seems to imply that if the font is symbolic the encoding
         // should be ignored, this doesn't appear to work for 'preistabelle.pdf'
diff --git a/test/pdfs/.gitignore b/test/pdfs/.gitignore
index da7078297..ab225f147 100644
--- a/test/pdfs/.gitignore
+++ b/test/pdfs/.gitignore
@@ -98,6 +98,7 @@
 !issue5747.pdf
 !issue6099.pdf
 !issue6336.pdf
+!issue6410.pdf
 !gradientfill.pdf
 !bug903856.pdf
 !bug850854.pdf
diff --git a/test/pdfs/issue6410.pdf b/test/pdfs/issue6410.pdf
new file mode 100644
index 000000000..c0b5ad946
Binary files /dev/null and b/test/pdfs/issue6410.pdf differ
diff --git a/test/test_manifest.json b/test/test_manifest.json
index c43095116..42c986196 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -1086,6 +1086,13 @@
       "link": true,
       "type": "eq"
     },
+    {  "id": "issue6410",
+       "file": "pdfs/issue6410.pdf",
+       "md5": "fd5c5898d5b9754bb546724b7d31bf59",
+       "rounds": 1,
+       "link": false,
+       "type": "eq"
+    },
     {  "id": "issue6413",
        "file": "pdfs/issue6413.pdf",
        "md5": "08926ac7a46e27a4abbb31256b3a7b29",