Web page data is ephemeral, while Web archiving has played a key role in preserving this valuable information for the future. Recent research on web archiving has focused on the consistency between archived data in a local system and real data in a remote Web server. These archiving methods are mainly designed for search-engine applications. However, since archiving data is preserved for future applications, we argue that the completeness of archived data is a more valuable factor for future utility. In this work, we study web-page archiving methods which aim at completeness of archived data with predefined available resources. First, we study an archiving method that assumes complete knowledge on web-page updates. While this assumption may not be realistic, the performance of this method provides an upper-bound for others which assume the unknown on web-page updates. We subsequently propose a practical archiving method without any knowledge assumption. Performance of this algorithm is compared. Meanwhile, our newly proposed algorithm is shown to significantly out-perform the periodic method that has been traditionally used in web archiving.