When a user views an archived page using the archive's user interface (UI), the user selects a datetime to view from a list. The archived web page, if available, is then displayed. From this display, the web archive UI attempts to simulate the web browsing experience by smoothly transitioning between archived pages. During this process, the target datetime changes with each link followed; drifting away from the datetime originally selected. When browsing sparsely-archived pages, this nearly-silent drift can be many years in just a few clicks. We conducted 200,000 acyclic walks of archived pages, following up to 50 links per walk, comparing the results of two target datetime policies. The Sliding Target policy allows the target datetime to change as it does in archive UIs such as the Internet Archive's Wayback Machine. The Sticky Target policy, represented by the Memento API, keeps the target datetime the same throughout the walk. We found that the Sliding Target policy drift increases with the number of walk steps, number of domains visited, and choice (number of links available). However, the Sticky Target policy controls temporal drift, holding it to less than 30 days on average regardless of walk length or number of domains visited. The Sticky Target policy shows some increase as choice increases, but this may be caused by other factors. We conclude that based on walk length, the Sticky Target policy generally produces at least 30 days less drift than the Sliding Target policy.