diff --git src/wp-includes/class-wp-customize-setting.php src/wp-includes/class-wp-customize-setting.php
index a16b100..7f1f98a 100644
--- src/wp-includes/class-wp-customize-setting.php
+++ src/wp-includes/class-wp-customize-setting.php
@@ -696,6 +696,15 @@ class WP_Customize_Setting {
 		$is_core_type = ( 'option' === $this->type || 'theme_mod' === $this->type );
 
 		if ( ! $is_core_type && ! $this->is_multidimensional_aggregated ) {
+
+			// Use post value if previewed and a post value is present.
+			if ( $this->is_previewed ) {
+				$value = $this->post_value( null );
+				if ( null !== $value ) {
+					return $value;
+				}
+			}
+
 			$value = $this->get_root_value( $this->default );
 
 			/**
diff --git src/wp-includes/customize/class-wp-customize-custom-css-setting.php src/wp-includes/customize/class-wp-customize-custom-css-setting.php
index eb9379e..eadd47c 100644
--- src/wp-includes/customize/class-wp-customize-custom-css-setting.php
+++ src/wp-includes/customize/class-wp-customize-custom-css-setting.php
@@ -132,10 +132,13 @@ final class WP_Customize_Custom_CSS_Setting extends WP_Customize_Setting {
 	 * @return string
 	 */
 	public function value() {
-		$id_base = $this->id_data['base'];
-		if ( $this->is_previewed && null !== $this->post_value( null ) ) {
-			return $this->post_value();
+		if ( $this->is_previewed ) {
+			$post_value = $this->post_value( null );
+			if ( null !== $post_value ) {
+				return $post_value;
+			}
 		}
+		$id_base = $this->id_data['base'];
 		$value = '';
 		$post = wp_get_custom_css_post( $this->stylesheet );
 		if ( $post ) {
diff --git tests/phpunit/tests/customize/setting.php tests/phpunit/tests/customize/setting.php
index 89b0720..03fd0c2 100644
--- tests/phpunit/tests/customize/setting.php
+++ tests/phpunit/tests/customize/setting.php
@@ -395,6 +395,18 @@ class Tests_WP_Customize_Setting extends WP_UnitTestCase {
 		$this->assertEquals( $post_data_overrides[ $name ], $this->custom_type_getter( $name, $this->undefined ) );
 		$this->assertEquals( $post_data_overrides[ $name ], $setting->value() );
 
+		// Custom type that does not handle supplying the post value from the customize_value_{$id_base} filter.
+		$setting_id = 'custom_without_previewing_value_filter';
+		$setting = $this->manager->add_setting( $setting_id, array(
+			'type' => 'custom_preview_test',
+			'default' => 123,
+			'sanitize_callback' => array( $this->manager->nav_menus, 'intval_base10' ),
+		) );
+		$this->assertSame( 123, $setting->value() );
+		$this->manager->set_post_value( $setting_id, '456' );
+		$setting->preview();
+		$this->assertSame( 456, $setting->value() );
+
 		unset( $this->custom_type_data_previewed, $this->custom_type_data_saved );
 	}