The tweaked format aims to inject new life into the struggling one-to-many messaging service by moving away from a pure chronological timeline to one determined by algorithm, as used by social network leader Facebook.
Twitter said the "Show me the best tweets first" feature is optional and that users can stick with tweets rushing by like leaves on a fast-moving river, if they prefer.
"You follow hundreds of people on Twitter -- maybe thousands -- and when you open Twitter, you may feel like you've missed their most important tweets," senior engineering manager Mike Jahr said in a blog post.
The algorithm was most likely built on a "while you were away" feature that Twitter introduced about a year ago to show people notable posts they missed while not using the service.
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"When you first open Twitter, the tweets you're most likely to care about will appear at the top of your timeline -- they are recent, and in reverse chronological order," Jahr said.
"Then the rest of the tweets will be displayed right underneath, also in reverse chronological order, as always."
With the new feature, "we've improved the timeline by analyzing how millions of people engage with billions of tweets," said product marketing manager Eric Farkas.
"We're using this information to determine the best content to surface. We use a person's past Twitter activity to predict which tweets they might like to see most."
The "Show me the best tweets first" feature is available to people accessing Twitter using a Web browser or applications on mobile devices powered by Apple or Android software.
"We've already noticed that people who have used this new feature tend to retweet and tweet more, which is good for everyone," Jahr said.
"If you love it, great," Jahr said. "If you don't, you can easily turn it off in settings.