Share story has begun dropping off food and other small items at doorsteps in San Francisco, its third city as it continues to look for ways to speed up delivery of the products it sells.

The company rolled out AmazonFresh there today, five months after debuting the service in Los Angeles. The company expanded into those cities only after testing its grocery delivery service in Seattle for nearly six years. And rumors persist that Amazon is considering launching Fresh in the New York metropolitan area soon.

The service helps Amazon move a step closer toward giving customers same-day delivery of the products it sells. That remains the biggest advantage brick-and-mortar rivals hold over the online giant, which can offer customers the sort of instant gratification that Amazon simply can’t match. It’s the reason why Amazon has been rapidly expanding the number of warehouses it operates, and why it cut a deal with the U.S. Postal Service to deliver goods on Sunday.

The company highlighted shipping speed in announcing the move into San Francisco.

“Place an order by 10 a.m. and get items by dinner, or order by 10 p.m. and get items by breakfast,” the company said in a statement.

While Fresh primarily caters to grocery shoppers, the company said consumers can select from more than 500,000 items, including books, toys and small electronics. Those items, which often carry higher margins that food, could make the service more viable than traditional grocery delivery.

As with the Los Angeles rollout, Fresh will be available by membership in Amazon Prime Fresh, and it’s not cheap. Shoppers who sign up for the service will be able to use it free for one month. After that trial period, they’ll need to pay $299 a year to continue to use the service. And they’ll need to spend $35 to get free delivery.

Included in that $299 fee is membership to Amazon Prime, the company’s free two-day shipping option for items purchased from its website. Prime members also get access to the company Netflix-like video-streaming service. Existing Prime members who sign up for Prime Fresh will have their $79-a-year membership fee refunded on a prorated basis.

Fresh customers in Seattle don’t pay an annual fee. While the company hasn’t explained the rationale for charging a membership fee in San Francisco and Los Angeles, it’s likely trying to tamp down use of the service as it figures out the most economic model to delivering goods within hours of their being ordered.

That caution is grounded in the fact that Amazon has taken so long to figure out the economics of the business in Seattle. What’s more, while several supermarket chains deliver food, a handful of Web startups that made a business of delivering groceries, such as Webvan, have failed.

Jay Greene: 206-464-2231 or Twitter: iamjaygreene