Same-day delivery not fast enough for you? Amazon is revving up its delivery service by offering one- and three-hour options in cities across the U.S., the e-commerce giant said Tuesday.

The move better positions Amazon to compete with big-box stores, local drugstores and other retailers that have responded to the growth in online shopping by leaning into faster delivery in recent years, GlobalData retail analyst Neil Saunders told CBS News.

"It's bad news for drugstores in particular," he said, noting that Amazon's prices are often superior for everyday staples like toothpaste or toilet paper.

Where is 1-hour and 3-hour delivery available?
Amazon's 1-hour delivery is now available in parts of Chicago; Houston; Los Angeles; Nashville, Tennessee; Oklahoma City, Oklahoma; and Washington, D.C., as well as in smaller cities including Des Moines, Iowa; Boise, Idaho; and American Fork, Utah.

Three-hour delivery is available in more than 2,000 large, midsize and small cities, and in suburbs like Cornwall, Pennsylvania; Harrah, Oklahoma; and Arabi, Louisiana, according to Amazon. The company plans to start offering accelerated delivery in other cities in the coming months (See here if the new delivery options are available where you live.)

What can I get delivered in under 3 hours?
A range of different products is eligible for expedited delivery, according to Amazon. They include household supplies like paper towels and toilet paper; health and beauty items; over-the-counter medications; electronics; toys; and clothing.

How much does it cost?
For members of Amazon's Prime shopping club, 1-hour delivery costs $9.99, while the 3-hour option runs $4.99. For non-Prime customers, 1-hour delivery costs $19.99 and 3-hour delivery is $14.99. Prime members may still have goods delivered same-day for free with their annual memberships.

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