diff --git a/src/wp-includes/pluggable.php b/src/wp-includes/pluggable.php
index d58f18940b..98403b34ae 100644
--- a/src/wp-includes/pluggable.php
+++ b/src/wp-includes/pluggable.php
@@ -26,8 +26,14 @@ if ( !function_exists('wp_set_current_user') ) :
 function wp_set_current_user($id, $name = '') {
 	global $current_user;
 
-	if ( isset( $current_user ) && ( $current_user instanceof WP_User ) && ( $id == $current_user->ID ) )
+	// If `$id` matches the user who's already current, there's nothing to do.
+	if ( isset( $current_user )
+		&& ( $current_user instanceof WP_User )
+		&& ( $id == $current_user->ID )
+		&& ( null !== $id )
+	) {
 		return $current_user;
+	}
 
 	$current_user = new WP_User( $id, $name );
 
diff --git a/tests/phpunit/tests/user/wpSetCurrentUser.php b/tests/phpunit/tests/user/wpSetCurrentUser.php
index c47c22cc74..b3c8fce918 100644
--- a/tests/phpunit/tests/user/wpSetCurrentUser.php
+++ b/tests/phpunit/tests/user/wpSetCurrentUser.php
@@ -23,5 +23,41 @@ class Tests_User_WpSetCurrentUser extends WP_UnitTestCase {
 		$this->assertEquals( $user, wp_get_current_user() );
 		$this->assertSame( $u, get_current_user_id() );
 	}
+
+	public function test_should_set_by_name_if_id_is_null_and_current_user_is_nonempty() {
+		$u1 = $this->factory->user->create();
+		wp_set_current_user( $u1 );
+		$this->assertSame( $u1, get_current_user_id() );
+
+		$u2 = $this->factory->user->create( array(
+			'user_login' => 'foo',
+		) );
+
+		$user = wp_set_current_user( null, 'foo' );
+
+		$this->assertSame( $u2, $user->ID );
+		$this->assertEquals( $user, wp_get_current_user() );
+		$this->assertSame( $u2, get_current_user_id() );
+	}
+
+	/**
+	 * Test that you can set the current user by the name parameter when the current user is 0.
+	 *
+	 * @ticket 20845
+	 */
+	public function test_should_set_by_name_if_id_is_null() {
+		wp_set_current_user( 0 );
+		$this->assertSame( 0, get_current_user_id() );
+
+		$u = $this->factory->user->create( array(
+			'user_login' => 'foo',
+		) );
+
+		$user = wp_set_current_user( null, 'foo' );
+
+		$this->assertSame( $u, $user->ID );
+		$this->assertEquals( $user, wp_get_current_user() );
+		$this->assertSame( $u, get_current_user_id() );
+	}
 }