diff --git a/src/evaluator.js b/src/evaluator.js
index 7e75ea904..1c41f8409 100644
--- a/src/evaluator.js
+++ b/src/evaluator.js
@@ -791,6 +791,10 @@ var PartialEvaluator = (function PartialEvaluatorClosure() {
           };
         }
 
+        var cidEncoding = baseDict.get('Encoding');
+        if (isName(cidEncoding))
+          properties.cidEncoding = cidEncoding.name;
+
         var cidToGidMap = dict.get('CIDToGIDMap');
         if (isStream(cidToGidMap))
           properties.cidToGidMap = this.readCidToGidMap(cidToGidMap);
diff --git a/src/fonts.js b/src/fonts.js
index 8177916cb..dda0c0df3 100644
--- a/src/fonts.js
+++ b/src/fonts.js
@@ -4126,6 +4126,15 @@ var Font = (function FontClosure() {
         } else
           cid++;
       }
+
+      var cidEncoding = properties.cidEncoding;
+      if (cidEncoding && cidEncoding.indexOf('Uni') === 0) {
+        // input is already Unicode for Uni* CMap encodings.
+        // However, Unicode-to-CID conversion is needed
+        // regardless of the CMap encoding. So we can't reset
+        // unicodeToCID.
+        this.cidToUnicode = [];
+      }
     },
 
     bindDOM: function Font_bindDOM() {
@@ -4205,16 +4214,12 @@ var Font = (function FontClosure() {
         case 'CIDFontType0':
           if (this.noUnicodeAdaptation) {
             width = this.widths[this.unicodeToCID[charcode] || charcode];
-            fontCharCode = mapPrivateUseChars(charcode);
-            break;
           }
           fontCharCode = this.toFontChar[charcode] || charcode;
           break;
         case 'CIDFontType2':
           if (this.noUnicodeAdaptation) {
             width = this.widths[this.unicodeToCID[charcode] || charcode];
-            fontCharCode = mapPrivateUseChars(charcode);
-            break;
           }
           fontCharCode = this.toFontChar[charcode] || charcode;
           break;