Amazon has reported that it has sold “millions” of Kindle Fires, despite receiving some complaints from users about performance. The exact numbers aren’t known, and sales figures seem to be rolled in with its other Kindle devices. Today, Amazon released the first Kindle Fire software update, with more promises of fixes to come.

According to a story from Fierce Mobile Content, the over-the-air update to the tablet’s software is available to all users with an Internet connection and should have some notable effects. One of the big problems users and reviewers have faced so far with the tablet is the responsiveness of the user interface. Here’s a quote from Amazon on a customer service forum discussing the update:

This update enhances fluidity and performance, improves touch navigation responsiveness, gives you the option to choose which items display on the carousel, and adds the ability to add a password lock on Wi-Fi access. The update will be automatically delivered to your Kindle Fire.

Hopefully the update will dish out some welcome improvements to the popular, affordably priced tablet. The trouble with the user interface has been a big stumbling block for the tablet, at least among tech reviewers. As FMC points out, usability expert Jakob Nielsen told The New York Times that he couldn’t recommend the Kindle Fire and thought it would end up being a failure.

But it seems Amazon customer loyalty coupled with a price tag that undercuts Apple’s iPad by some $300 are still bringing in the customers, although Amazon won’t say how many. It has said that the Kindle Fire is its best-selling device ever, which is notable because the entire Kindle line is pretty popular. Of Kindle devices in general, Amazon said last week that it has been selling more than 1 million per week for the last three weeks, but it’s not clear what segment of that number is made up by the Android tablet.

Hoewever, there appears to be no fix yet to the web browsing experience. Users and reviewers have reported that one of Amazon’s big selling points for the device, Amazon Silk, isn’t really up to snuff right now. Silk is a cloud-based service that allows the technically low-powered Kindle Fire to load websites faster by sharing the burden of processing the data with Amazon’s servers over the Internet. A remote server processes the web page and sends the completed page to the tablet – or at least, that’s how it works in theory. In practice, web browsing is another segment of the Fire experience that’s leaving users wanting more.

Amazon has promised more fixes to come, but with the holidays approaching it’ll probably be a while. In the meantime, if all goes well with the current update, it’ll likely help users giving the gift of the Fire this holiday, and satisfied users will mean more sales for Amazon.