Index: wp-includes/functions.php
===================================================================
--- wp-includes/functions.php	(revision 23195)
+++ wp-includes/functions.php	(working copy)
@@ -924,10 +924,10 @@
  */
 function nocache_headers() {
 	$headers = wp_get_nocache_headers();
+	if ( isset( $headers['Last-Modified'] ) && empty( $headers['Last-Modified'] ) )
+		unset( $headers['Last-Modified'] );
 	foreach( $headers as $name => $field_value )
 		@header("{$name}: {$field_value}");
-	if ( empty( $headers['Last-Modified'] ) && function_exists( 'header_remove' ) )
-		@header_remove( 'Last-Modified' );
 }
 
 /**
Index: wp-includes/class-wp.php
===================================================================
--- wp-includes/class-wp.php	(revision 23195)
+++ wp-includes/class-wp.php	(working copy)
@@ -376,14 +376,14 @@
 
 		$headers = apply_filters('wp_headers', $headers, $this);
 
+		if ( isset( $headers['Last-Modified'] ) && empty( $headers['Last-Modified'] ) )
+			unset( $headers['Last-Modified'] );
+
 		if ( ! empty( $status ) )
 			status_header( $status );
 		foreach( (array) $headers as $name => $field_value )
 			@header("{$name}: {$field_value}");
 
-		if ( isset( $headers['Last-Modified'] ) && empty( $headers['Last-Modified'] ) && function_exists( 'header_remove' ) )
-			@header_remove( 'Last-Modified' );
-
 		if ( $exit_required )
 			exit();