diff --git a/src/wp-includes/plugin.php b/src/wp-includes/plugin.php
index 27a65ee1b5..06d727f313 100644
--- a/src/wp-includes/plugin.php
+++ b/src/wp-includes/plugin.php
@@ -325,10 +325,10 @@ function remove_all_filters( $tag, $priority = false ) {
 	global $wp_filter, $merged_filters;
 
 	if ( isset( $wp_filter[ $tag ]) ) {
-		if ( false !== $priority && isset( $wp_filter[ $tag ][ $priority ] ) ) {
-			$wp_filter[ $tag ][ $priority ] = array();
-		} else {
+		if ( false === $priority ) {
 			$wp_filter[ $tag ] = array();
+		} else if ( isset( $wp_filter[ $tag ][ $priority ] ) ) {
+			$wp_filter[ $tag ][ $priority ] = array();
 		}
 	}
 
diff --git a/tests/phpunit/tests/filters.php b/tests/phpunit/tests/filters.php
index c0eb1250c7..d9eda55a2b 100644
--- a/tests/phpunit/tests/filters.php
+++ b/tests/phpunit/tests/filters.php
@@ -196,6 +196,25 @@ class Tests_Filters extends WP_UnitTestCase {
 		$this->assertEquals(array($tag), $a->get_tags());
 	}
 
+	/**
+	 * @ticket 20920
+	 */
+	function test_remove_all_filters_should_respect_the_priority_argument() {
+		$a = new MockAction();
+		$tag = rand_str();
+		$val = rand_str();
+
+		add_filter( $tag, array( $a, 'filter' ), 12 );
+		$this->assertTrue( has_filter( $tag ) );
+
+		// Should not be removed.
+		remove_all_filters( $tag, 11 );
+		$this->assertTrue( has_filter( $tag ) );
+
+		remove_all_filters( $tag, 12 );
+		$this->assertFalse( has_filter( $tag ) );
+	}
+
 	/**
 	 * @ticket 9886
 	 */