diff --git a/src/wp-includes/pluggable.php b/src/wp-includes/pluggable.php
index ecacab460e..88d1440599 100644
--- a/src/wp-includes/pluggable.php
+++ b/src/wp-includes/pluggable.php
@@ -1458,7 +1458,7 @@ function wp_notify_postauthor( $comment_id, $deprecated = null ) {
 	// we want to reverse this for the plain text arena of emails.
 	$blogname = wp_specialchars_decode(get_option('blogname'), ENT_QUOTES);
 	$comment_content = wp_specialchars_decode( $comment->comment_content );
-	
+
 	switch ( $comment->comment_type ) {
 		case 'trackback':
 			$notify_message  = sprintf( __( 'New trackback on your post "%s"' ), $post->post_title ) . "\r\n";
@@ -1737,8 +1737,7 @@ if ( !function_exists('wp_new_user_notification') ) :
  * @param int    $user_id    User ID.
  * @param null   $deprecated Not used (argument deprecated).
  * @param string $notify     Optional. Type of notification that should happen. Accepts 'admin' or an empty
- *                           string (admin only), or 'both' (admin and user). The empty string value was kept
- *                           for backward-compatibility purposes with the renamed parameter. Default empty.
+ *                           string (admin only), or 'both' (admin and user). Default empty.
  */
 function wp_new_user_notification( $user_id, $deprecated = null, $notify = '' ) {
 	if ( $deprecated !== null ) {
@@ -1758,7 +1757,8 @@ function wp_new_user_notification( $user_id, $deprecated = null, $notify = '' )
 
 	@wp_mail(get_option('admin_email'), sprintf(__('[%s] New User Registration'), $blogname), $message);
 
-	if ( 'admin' === $notify || empty( $notify ) ) {
+	// `$deprecated was pre-4.3 `$plaintext_pass`. An empty `$plaintext_pass` didn't sent a user notifcation.
+	if ( 'admin' === $notify || ( empty( $deprecated ) && empty( $notify ) ) ) {
 		return;
 	}
 
diff --git a/tests/phpunit/tests/user.php b/tests/phpunit/tests/user.php
index d122617be1..3644ffcb79 100644
--- a/tests/phpunit/tests/user.php
+++ b/tests/phpunit/tests/user.php
@@ -1040,8 +1040,48 @@ class Tests_User extends WP_UnitTestCase {
 	 * @ticket 33654
 	 * @expectedDeprecated wp_new_user_notification
 	 */
-	function test_wp_new_user_notification_old_signature_throws_deprecated_warning() {
-		wp_new_user_notification( self::$author_id, 'this_is_deprecated' );
+	function test_wp_new_user_notification_old_signature_throws_deprecated_warning_but_sends() {
+		unset( $GLOBALS['phpmailer']->mock_sent );
+
+		$was_admin_email_sent = false;
+		$was_user_email_sent = false;
+		wp_new_user_notification( self::$contrib_id, 'this_is_a_test_password' );
+
+		/*
+		 * Check to see if a notification email was sent to the
+		 * post author `blackburn@battlefield3.com` and and site admin `admin@example.org`.
+		 */
+		if ( ! empty( $GLOBALS['phpmailer']->mock_sent ) ) {
+			$was_admin_email_sent = ( isset( $GLOBALS['phpmailer']->mock_sent[0] ) && WP_TESTS_EMAIL == $GLOBALS['phpmailer']->mock_sent[0]['to'][0][0] );
+			$was_user_email_sent = ( isset( $GLOBALS['phpmailer']->mock_sent[1] ) && 'blackburn@battlefield3.com' == $GLOBALS['phpmailer']->mock_sent[1]['to'][0][0] );
+		}
+
+		$this->assertTrue( $was_admin_email_sent );
+		$this->assertTrue( $was_user_email_sent );
 	}
 
+	/**
+	 * Set up a user and try sending a notification using `wp_new_user_notification( $user );`.
+	 *
+	 * @ticket 34377
+	 */
+	function test_wp_new_user_notification_old_signature_no_password() {
+		unset( $GLOBALS['phpmailer']->mock_sent );
+
+		$was_admin_email_sent = false;
+		$was_user_email_sent = false;
+		wp_new_user_notification( self::$contrib_id );
+
+		/*
+		 * Check to see if a notification email was sent to the
+		 * post author `blackburn@battlefield3.com` and and site admin `admin@example.org`.
+		 */
+		if ( ! empty( $GLOBALS['phpmailer']->mock_sent ) ) {
+			$was_admin_email_sent = ( isset( $GLOBALS['phpmailer']->mock_sent[0] ) && WP_TESTS_EMAIL == $GLOBALS['phpmailer']->mock_sent[0]['to'][0][0] );
+			$was_user_email_sent = ( isset( $GLOBALS['phpmailer']->mock_sent[1] ) && 'blackburn@battlefield3.com' == $GLOBALS['phpmailer']->mock_sent[1]['to'][0][0] );
+		}
+
+		$this->assertTrue( $was_admin_email_sent );
+		$this->assertFalse( $was_user_email_sent );
+	}
 }