The company is expanding the Sunday delivery service it launched in November in Los Angeles and New York through a partnership with the U.S. Postal Service. The newly-eligible locations include Dallas, New Orleans and Philadelphia, as well as a dozen other cities across Indiana, Kentucky, Louisiana, Ohio, Oklahoma and Texas.

Where the service is available, customers will get a notice at checkout alerting them to the option of having packages delivered on a Sunday at no extra charge. Members of Amazon Prime can even order items as late as Friday to have them show up on their doorsteps on Sunday.

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Amazon says “millions of packages have been delivered on Sunday” since the service launched last fall and the company has plans to continue rolling out the delivery service to new regions in the U.S. at some point in 2014. An Amazon spokeswoman could not confirm details of the next planned expansion of the service, but reiterated the company’s previous statement that it will cover “a large portion of the U.S. population.” (In November, the company said, specifically, that it would eventually target Dallas and New Orleans, along with Houston and Phoenix, so customers in the latter two cities can probably expect the service to hit their areas at some point in the future.)

Mike Roth, Amazon’s vice president of North American operations said in a statement that Sunday package delivery has proven especially popular with families ordering baby supplies, including clothing, books and toys. “Sunday delivery is clearly crossing errands off the weekend to-do list,” he said.

In March, Amazon hiked the rates for its Prime membership service, which offers unlimited two-day shipping on a number of items along with other perks. The annual price of the Prime service jumped from $79 to $99, with the company blaming the price rise on increased fuel and shipping costs. Both FedEx (FDX) and UPS (UPS) said recently that they are raising their rates for shipping packages, with the former announcing higher fuel surcharges last week as well as a plan to begin charging for packages based on their dimensions, in addition to weight.

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In addition to expanding its Sunday service, Amazon recently launched Prime Pantry, a service that allows customers to buy several household products for a flat, $5.99 delivery fee, combining their purchases in one package measuring four cubic feet. The company even offers same-day delivery in about a dozen cities.

Amazon also said this week it will partner with Twitter to offer U.S. users of the social media site the option of adding products to their Amazon shopping cart by replying to a product link with the hashtag #AmazonCart. Customers will eventually need to visit Amazon.com to complete a transaction, but this presumably means certain Amazon customers will now be able to tweet on a Friday and have a package arrive on Sunday.