Microsoft seemingly has begun rolling out at least part of an awaited firmware update for its second-generation Surface Pro 2 tablets, according to user reports on Twitter and in various online forums.

However, the firmware update may be one of multiple updates or a partial update only, said sources close to the company.

The firmware update some report they are seeing -- designed to fix problems introduced by a faulty December 2013 update to Microsoft's newest Intel-based tablets -- seemingly is arriving in waves. Surface Pro 2 users in several countries across the world were reporting that they received an update starting the evening of January 17; others said an update arrived for download on their Surface Pro 2s on January 18.

Microsoft's December firmware update for its Surface Pro 2s resulted in a number of systems experiencing battery-life and sleep/shutdown issues. Microsoft ended up pulling the firmware update and officials have been saying a fix would come some time after the holidays.

Earlier this week, Microsoft did issue firmware updates for first-generation Surface Pro devices that were experiencing battery-life problems due to issues with the Type and Touch covers. Microsoft first released a Surface Pro firmware update on January 14 for Surface Pros running Windows 8.0 and on January 15 for Surface Pros running Windows 8.1.

Microsoft officials had nothing new to say earlier this week as to when to expect the Surface Pro 2 firmware fix beyond that it would be released as soon as possible.

A couple of my Twitter chums said they received over the past few hours a firmware update for their Surface Pro 2s, but no specifics as to what it fixed or included. The screen shot embedded in this post is from one of those users, @JulianKay; another notification came from @JustinHeatherington.

User Phra Mick Ratanapanyo reported on Microsoft's Answers Forum that he had installed the January 18 2014 Firmware update on an Surface Pro 2 and that "Wifi, Bluetooth, pen & Type Cover 2 all functioning well."

However, that user also noted that one old problem -- cold booting with a microSD card still -- still was causing excessive CPU consumption issues. Heatherington confirmed the same regarding the cold-booting problem after applying the January 2014 Surface Pro 2 firmware update.

I've asked Microsoft officials to confirm that the firmware update that is rolling out for Surface Pro 2 is the awaited fix for the battery-life/cover problems reported in December. I've also asked for an update as to when all Surface Pro 2 users should get the firmware update. I will update this post with an official response if and when I hear back.

Update (January 19): Here's Microsoft's statement, courtesy of a company spokesperson. Tgise who didn't install the faulty December firmware update don't need and won't receive the January patch, officials said.

“This weekend we released an update that addresses the unexpected wake and battery drain behavior experienced by a small number of Surface Pro 2 customers who installed the December Windows Update. This should have no impact on customers who had not received the December update. We are working hard to deliver the rest of the December update to those customers who had not received it prior to it being removed from distribution.”

Update (January 21): Microsoft has updated the Surface Pro 2 Update history page to reflect the existence of a firmware update. From the page:

January 2014 update

Updated UEFI firmware, version 2.04.0350, to resolve behavior where the Surface failed to enter sleep while idle, negatively impacting battery life.