As usual, (AMZN) - Get, Inc. Report was selective about what it chose to share through its annual post-Christmas PR about its holiday season. But the PR's 101 bullet points, together with the three paragraphs that preceded them, still turned up a decent amount of useful info about Jeff Bezos' company.

Last week, I offered some takeaways -- from recent Amazon announcements as well as third-party research -- regarding the company's pricing, warehouse efficiency, same-day delivery footprint, ad spending and private-label goods sales this holiday season. Here are a few additional takeaways about what the company was up to between Thanksgiving and Christmas.

Amazon's mobile sales took off.

Amazon states global shopping on its core app rose nearly 70% during the holiday season. Notably, that's faster than the 56% growth the company reported for the 2016 holiday season. This follows data from Adobe Systems (ADBE) - Get Adobe Inc. Report , e-commerce ad firm Criteo (CRTO) - Get Criteo SA Sponsored ADR Report and others indicating mobile shopping volumes rose sharply during Thanksgiving weekend, as well as a summer survey from comScore indicating 34% of U.S. smartphone users "cannot go without" Amazon's app, a number trailing only Facebook's (FB) - Get Facebook, Inc. Class A Report core app and the Gmail app.

The growing willingness of Amazon customers to use its app to place orders, rather than solely relying on its PC website, brings several indirect benefits. Among them: It ups the likelihood of show-rooming (i.e., buying items on Amazon after seeing them in physical stores); it fuels share gains against online retailers whose apps aren't widely installed and/or as popular for shopping; it lets Amazon promote deals via mobile notifications; and (though Amazon has been more willing lately to spend on Alphabet/Google (GOOGL) - Get Alphabet Inc. Class A Report shopping ads) it makes the company less dependent on search traffic.

Amazon's warehouse and logistics footprints continue growing rapidly.

This is hardly shocking, given the paces at which Amazon has been growing its fulfillment and capital spending. But the company's latest numbers are still fairly impressive: Amazon grew its fulfillment and shipping network square footage by over 30% in 2017, and its U.S. logistics footprint now includes over 6,000 truck trailers and 32 Amazon Air (formerly Prime Air) planes.

The 32 planes are up from 25 as of this summer; in 2016, Amazon inked deals to lease 40 Boeing (BA) - Get Boeing Company Report 767 planes. In late 2015, the company said it had bought "thousands" of truck trailers that would bear its logo and (with the help of third-party trucking firms) moves goods between Amazon warehouses, but hadn't shared a precise number.

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Echo and Fire TV sales apparently jumped, and developers will probably take notice.

Though it still refuses to break out Echo speaker sales, Amazon says it sold "tens of millions" of "Alexa-enabled devices" -- a category that covers the Echo line, Fire tablets and Fire TV set-tops and HDMI sticks. The company also states the puck-shaped Echo Dot speaker, which has been priced at just $30 through a holiday season promo, was "the best-selling product from any manufacturer in any category across all of Amazon, with millions sold."

For comparison, research firm Strategy Analytics forecast in October about 16 million Alexa-powered smart speakers would be sold over the whole of 2017, giving Amazon a 68% market share. The Echo Dot's low price (low enough to make the device an impulse buy), together with the strength of the Alexa ecosystem and Amazon's ability to give the Echo lines tons of free advertising, seems to have yielded an inflection point for its smart speaker sales.

Amazon also declares -- in a shot at Roku (ROKU) - Get Roku, Inc. Class A Report , whose shares blasted off in November following strong results and guidance -- that it sold more than twice as many Fire TV sticks as it did last holiday season, and that Fire TV "continues to be the #1 streaming media player family in the U.S., U.K., Germany, and Japan, across all retailers."

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In addition, Amazon's PR features several bullet points touting the usage growth seen by its Alexa voice assistant. Among the datapoints: Alexa music listening rose 200% from a year ago; "millions" of Prime members users Alexa to shop; and Alexa usage on Fire TV devices rose 889% in the U.S..

The Echo, Fire TV and Alexa stats aren't just meant to please investors, but also convince developers to support Alexa -- whether by creating Alexa "skills," launching Alexa-powered devices or building smart home hardware that can be controlled by Alexa. Though Google Assistant remains a formidable long-term rival due to Google's AI strengths, search integration and mobile footprint, Alexa has clearly stolen a march on rivals when it comes to home devices.

Small businesses are big business for Amazon.

A few weeks after stating it sold close to 140 million items to "small businesses and entrepreneurs" from Thanksgiving through Cyber Monday, Amazon disclosed it sold over 1 billion items to them over the holiday season. From the looks of things, many small businesses turn to Amazon as reflexively for their shopping needs as consumers.

The holiday sales follow the October launch of Business Prime Shipping, a service (currently available in the U.S. and Germany) that provides free 2-day shipping on business items. The service costs $499 per year for companies looking to sign up 10 or fewer workers, and just $1,299 for companies looking to sign up 11 to 100 workers. Those looking to sign up over 100 workers are charged $10,099.

Amazon is delivering a lot more items in one day or less.

As the average distance between the point of fulfillment and point of delivery keeps dropping thanks to Amazon's non-stop warehouse-building, and as Amazon's sales growth leads the scale of its delivery operations for a given city or town to grow, it follows that it becomes more economical for the company to deliver many items within a day or less. Amazon notes shipments of of items via free one-day shipping, free same-day shipping or the Prime Now service (delivery in two hours or less) more than doubled this holiday season.

The disclosure comes two weeks after Amazon said its same-day and one-day delivery services are now available in over 8,000 cities and towns, up from just 5,000 earlier in 2017 and 1,000 as of June 2016. Amazon still faces some challenges in making Prime Now, which now carries a $35 order minimum for free shipping and relies on Uber-like contractors to deliver orders, economical on a large scale. But it appears to have the formula figured out for same-day and one-day services, and that provides a major competitive advantage.

This column originally appeared on Dec. 27 on Real Money, our premium site for active traders. Click here to get more great columns like this.

Jim Cramer and the AAP team hold positions in Alphabet and Facebook for their Action Alerts PLUS Charitable Trust Portfolio. Want to be alerted before Cramer buys or sells GOOGL or FB? Learn more now.

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