diff --git a/lib/classes/upgrade/util.php b/lib/classes/upgrade/util.php
index c3009010825..2c14e983b40 100644
--- a/lib/classes/upgrade/util.php
+++ b/lib/classes/upgrade/util.php
@@ -86,7 +86,9 @@ final class util {
      * @return bool
      */
     public static function can_use_tls12(array $curlinfo, $uname) {
-        if ($curlinfo['version_number'] < 467456 || !defined('CURL_SSLVERSION_TLSv1_2')) {
+        // Do not compare the cURL version, e.g. $curlinfo['version_number'], with v7.34.0 (467456):
+        // some Linux distros backport security issues and keep lower version numbers.
+        if (!defined('CURL_SSLVERSION_TLSv1_2')) {
             return false;
         }
 
diff --git a/lib/tests/upgrade_util_test.php b/lib/tests/upgrade_util_test.php
index bba4cebcd0c..50aa91930b8 100644
--- a/lib/tests/upgrade_util_test.php
+++ b/lib/tests/upgrade_util_test.php
@@ -24,7 +24,7 @@
 
 defined('MOODLE_INTERNAL') || die();
 
-// Hack to let tests run on travis..
+// Hack to let tests run on Travis CI.
 defined('CURL_SSLVERSION_TLSv1_2') || define('CURL_SSLVERSION_TLSv1_2', 6);
 
 /**
@@ -36,16 +36,6 @@ defined('CURL_SSLVERSION_TLSv1_2') || define('CURL_SSLVERSION_TLSv1_2', 6);
  */
 class upgrade_util_testcase extends advanced_testcase {
 
-    /**
-     * A cURL version that supports TLS 1.2.
-     */
-    const VALID_CURL_VERSION = 467456;
-
-    /**
-     * A cURL version that does not support TLS 1.2.
-     */
-    const INVALID_CURL_VERSION = 467455;
-
     /**
      * The value of PHP_ZTS when thread safety is enabled.
      */
@@ -132,17 +122,11 @@ class upgrade_util_testcase extends advanced_testcase {
 
         // Set the curl values we are testing to the passed data.
         $curlinfo['ssl_version'] = $sslversion;
-        $curlinfo['version_number'] = self::VALID_CURL_VERSION;
 
         // Set uname to system value if none passed in test case.
         $uname = !empty($uname) ? $uname : php_uname('r');
 
         $this->assertSame($expected, \core\upgrade\util::can_use_tls12($curlinfo, $uname));
-
-        // Now set the curl version to outdated one.
-        $curlinfo['version_number'] = self::INVALID_CURL_VERSION;
-        // Tls12 should never be possible now curl version is bad.
-        $this->assertFalse(\core\upgrade\util::can_use_tls12($curlinfo, $uname));
     }
 
     /**