diff --git a/include/qpdf/QPDFTokenizer.hh b/include/qpdf/QPDFTokenizer.hh
index b04e4d8..a0e1824 100644
--- a/include/qpdf/QPDFTokenizer.hh
+++ b/include/qpdf/QPDFTokenizer.hh
@@ -197,7 +197,6 @@ class QPDFTokenizer
     bool isSpace(char);
     bool isDelimiter(char);
     void findEI(std::shared_ptr<InputSource> input);
-    void handleCharacter(char);
 
     enum state_e {
         st_top,
@@ -212,6 +211,8 @@ class QPDFTokenizer
         st_token_ready
     };
 
+    void handleCharacter(char);
+    void inHexstring(char);
     void reset();
 
     // Lexer state
diff --git a/libqpdf/QPDFTokenizer.cc b/libqpdf/QPDFTokenizer.cc
index 6c83119..1220e01 100644
--- a/libqpdf/QPDFTokenizer.cc
+++ b/libqpdf/QPDFTokenizer.cc
@@ -331,7 +331,8 @@ QPDFTokenizer::handleCharacter(char ch)
             return;
         }
         this->state = st_in_hexstring;
-        break;
+        inHexstring(ch);
+        return;
 
     case st_gt:
         if (ch == '>') {
@@ -469,13 +470,18 @@ QPDFTokenizer::handleCharacter(char ch)
         return;
 
     case (st_in_hexstring):
-        break;
+        inHexstring(ch);
+        return;
 
     default:
         throw std::logic_error(
             "INTERNAL ERROR: invalid state while reading token");
     }
+}
 
+void
+QPDFTokenizer::inHexstring(char ch)
+{
     if (ch == '>') {
         this->type = tt_string;
         this->state = st_token_ready;