diff --git a/src/core/fonts.js b/src/core/fonts.js
index 355aca39956c48..00bd9d4d69735f 100644
--- a/src/core/fonts.js
+++ b/src/core/fonts.js
@@ -1610,7 +1610,12 @@ var Font = (function FontClosure() {
             continue;
           }
 
-          if (platformId === 0 && encodingId === 0) {
+          if (
+            platformId === 0 &&
+            (encodingId === 0 || // Unicode Default
+            encodingId === 1 || // Unicode 1.1
+              encodingId === 3) // Unicode BMP
+          ) {
             useTable = true;
             // Continue the loop since there still may be a higher priority
             // table.
@@ -2793,24 +2798,17 @@ var Font = (function FontClosure() {
         var cmapMappings = cmapTable.mappings;
         var cmapMappingsLength = cmapMappings.length;
 
-        // 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'
-        // where the the font is symbolic and it has an encoding.
+        // If the font has an encoding and is not symbolic then follow the
+        // rules in section 9.6.6.4 of the spec on how to map 3,1 and 1,0
+        // cmaps. If no preferred cmap is found we also fallback to this code
+        // since it can use differences and the post table to create mappings.
         if (
           (properties.hasEncoding &&
+            !this.isSymbolicFont &&
             ((cmapPlatformId === 3 && cmapEncodingId === 1) ||
               (cmapPlatformId === 1 && cmapEncodingId === 0))) ||
-          (cmapPlatformId === -1 &&
-          cmapEncodingId === -1 && // Temporary hack
-            !!getEncoding(properties.baseEncodingName))
+          (cmapPlatformId === -1 && cmapEncodingId === -1)
         ) {
-          // Temporary hack
-          // When no preferred cmap table was found and |baseEncodingName| is
-          // one of the predefined encodings, we seem to obtain a better
-          // |charCodeToGlyphId| map from the code below (fixes bug 1057544).
-          // TODO: Note that this is a hack which should be removed as soon as
-          //       we have proper support for more exotic cmap tables.
-
           var baseEncoding = [];
           if (
             properties.baseEncodingName === "MacRomanEncoding" ||
@@ -2834,6 +2832,7 @@ var Font = (function FontClosure() {
             if (!glyphName) {
               continue;
             }
+
             // Ensure that non-standard glyph names are resolved to valid ones.
             standardGlyphName = recoverGlyphName(glyphName, glyphsUnicodeMap);
 
@@ -2867,7 +2866,7 @@ var Font = (function FontClosure() {
               }
             }
           }
-        } else if (cmapPlatformId === 0 && cmapEncodingId === 0) {
+        } else if (cmapPlatformId === 0) {
           // Default Unicode semantics, use the charcodes as is.
           for (let i = 0; i < cmapMappingsLength; ++i) {
             charCodeToGlyphId[cmapMappings[i].charCode] =
diff --git a/test/pdfs/.gitignore b/test/pdfs/.gitignore
index 3da0e6caba35d9..8b3ad5998351a4 100644
--- a/test/pdfs/.gitignore
+++ b/test/pdfs/.gitignore
@@ -88,6 +88,7 @@
 !issue10665_reduced.pdf
 !issue11016_reduced.pdf
 !issue11045.pdf
+!bug1057544.pdf
 !issue11150_reduced.pdf
 !issue11242_reduced.pdf
 !issue11279.pdf
@@ -192,6 +193,7 @@
 !issue4260_reduced.pdf
 !bug1250079.pdf
 !bug1473809.pdf
+!issue12120_reduced.pdf
 !pdfjsbad1586.pdf
 !freeculture.pdf
 !issue6006.pdf
diff --git a/test/pdfs/bug1057544.pdf b/test/pdfs/bug1057544.pdf
new file mode 100644
index 00000000000000..4c1611c4cba493
Binary files /dev/null and b/test/pdfs/bug1057544.pdf differ
diff --git a/test/pdfs/issue12120_reduced.pdf b/test/pdfs/issue12120_reduced.pdf
new file mode 100644
index 00000000000000..7f791793aea0a9
Binary files /dev/null and b/test/pdfs/issue12120_reduced.pdf differ
diff --git a/test/test_manifest.json b/test/test_manifest.json
index 9a9370bd84be7b..3f56139dd57fb0 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -1991,6 +1991,12 @@
        "type": "eq",
        "about": "MediaBox and CropBox with indirect objects."
     },
+    {  "id": "bug1057544",
+       "file": "pdfs/bug1057544.pdf",
+       "md5": "49ad71b82ead1ee0fe4ddb41aa9e30b4",
+       "rounds": 1,
+       "type": "eq"
+    },
     {  "id": "issue2642",
       "file": "pdfs/issue2642.pdf",
       "md5": "b6679861fdce3bbab0c1fa51bb7f5077",
@@ -4204,6 +4210,12 @@
        "lastPage": 2,
        "type": "eq"
     },
+    {  "id": "issue12120_reduced",
+       "file": "pdfs/issue12120_reduced.pdf",
+       "md5": "b4570dcee26ac3121ad3322e19ed1a6a",
+       "rounds": 1,
+       "type": "eq"
+    },
     {  "id": "issue4883",
       "file": "pdfs/issue4883.pdf",
       "md5": "2fac0d9a189ca5fcef8626153d050be8",