When a media client is receiving a media stream, the media client determines an upcoming time point at which the media client is to perform a content revision involving insertion (e.g., substitution or overlaying) of new content. The media client further determines an advanced time point when the media client should initiate a process of acquiring the new content, setting the advanced time point sufficiently in advance of the upcoming content-revision time point to enable the media client to obtain at least enough of the new content to be able to start the content revision on time. In an example implementation, the media client could determine the advanced time point by predicting how long the content-acquisition process will take, based on consideration of past instances of content acquisition, possibly correlated with operational factors such as content source, processor load, memory load, network speed, and time of day.