diff --git a/src/PHPMailer.php b/src/PHPMailer.php
index 5ccf8ff..7672b84 100644
--- a/src/PHPMailer.php
+++ b/src/PHPMailer.php
@@ -3768,7 +3768,8 @@ class PHPMailer
                 break;
         }
 
-        if ($this->has8bitChars($str)) {
+        //ISO-2022 charsets such as ISO-2022-JP are 7-bit, but text using their escape sequences isn't us-ascii
+        if ($this->has8bitChars($str) || strpos($str, "\x1B") !== false) {
             $charset = $this->CharSet;
         } else {
             $charset = static::CHARSET_ASCII;
diff --git a/test/PHPMailer/EncodeHeaderTest.php b/test/PHPMailer/EncodeHeaderTest.php
new file mode 100644
index 0000000..dc8bcee
--- /dev/null
+++ b/test/PHPMailer/EncodeHeaderTest.php
@@ -0,0 +1,72 @@
+<?php
+
+/**
+ * PHPMailer - PHP email transport unit tests.
+ * PHP version 5.5.
+ *
+ * @author    Marcus Bointon <phpmailer@synchromedia.co.uk>
+ * @author    Andy Prevost
+ * @copyright 2012 - 2020 Marcus Bointon
+ * @copyright 2004 - 2009 Andy Prevost
+ * @license   https://www.gnu.org/licenses/old-licenses/lgpl-2.1.html GNU Lesser General Public License
+ */
+
+namespace PHPMailer\Test\PHPMailer;
+
+use PHPMailer\Test\TestCase;
+
+/**
+ * Test the charset label chosen when encoding header values.
+ *
+ * @covers \PHPMailer\PHPMailer\PHPMailer::encodeHeader
+ */
+final class EncodeHeaderTest extends TestCase
+{
+    /**
+     * Test the charset label used for 7-bit header values.
+     *
+     * @dataProvider dataEncodeHeaderCharset
+     *
+     * @param string $input    The header value to encode.
+     * @param string $expected The expected function return value.
+     * @param string $charset  The charset to use.
+     */
+    public function testEncodeHeaderCharset($input, $expected, $charset)
+    {
+        $this->Mail->CharSet = $charset;
+
+        self::assertSame($expected, $this->Mail->encodeHeader($input));
+    }
+
+    /**
+     * Data provider.
+     *
+     * @return array
+     */
+    public static function dataEncodeHeaderCharset()
+    {
+        return [
+            'ISO-2022-JP text keeps its charset label even though it is 7-bit' => [
+                //"Test" in Japanese katakana, converted to ISO-2022-JP
+                'input'    => "\x1B\$B%F%9%H\x1B(B",
+                'expected' => '=?ISO-2022-JP?Q?=1B$B%F%9%H=1B(B?=',
+                'charset'  => 'ISO-2022-JP',
+            ],
+            'ISO-2022-JP text in the middle of ASCII text keeps its charset label' => [
+                'input'    => "Re: \x1B\$B%F%9%H\x1B(B",
+                'expected' => '=?ISO-2022-JP?Q?Re:_=1B$B%F%9%H=1B(B?=',
+                'charset'  => 'ISO-2022-JP',
+            ],
+            'Plain ASCII text with an ISO-2022-JP charset is not encoded' => [
+                'input'    => 'Test',
+                'expected' => 'Test',
+                'charset'  => 'ISO-2022-JP',
+            ],
+            'ASCII text with a control character still falls back to us-ascii' => [
+                'input'    => "Joe\x7FBloggs",
+                'expected' => '=?us-ascii?Q?Joe=7FBloggs?=',
+                'charset'  => 'utf-8',
+            ],
+        ];
+    }
+}