The Google+ team, facing strong demand for the new social-networking service, has expansion on its mind.

Google briefly let Google+ users invite new members last night in a plan to double the social network's population. And Google has begun detailing its plans for letting business users, not just individuals, use the service starting later this year.

Google has been limiting the individual sign-up rate, leading to frustration among many who want to get in. But Dave Besbris, the Google+ engineering director, said last night it was time for another growth spurt.

"Things are going well with the systems right now so we feel comfortable enough to open up invites for a brief period. Our goal is to double the user base in the field trial from its initial group," he said in a Google+ post.

Apparently the moment was indeed fleeting, because I couldn't find an invitation mechanism by the time I woke up here in England. That means Lutz Beyer's amusing cartoon about Google+ exclusivity remains relevant.

Google had opened invitations briefly last week, shortly after the mostly-closed beta test began. I've had success getting quite a few people in by a somewhat circuitous Google+ invitation route that involves sharing a Google+ post by e-mail with their Gmail addresses.

It's been an irregular process: some people told me they never got an invitation, and sometimes the message took days to arrive. And because Google throttles the sign-up rate, many of those I've invited had to check back several times before they happened to click when the window was open.

In a comment, Besbris apologized for the sporadic availability.

"We are also ensuring, as we grow, things keep working well, so occasionally we may have to pause/slow down/speed up the signup rate to keep the service smooth and fast. The combo can make it seem unpredictable," he said. "I'm sorry [about] that and thanks for your patience."

An official invitation clearly would be a far better way to handle this than the e-mail technique. Google, though, is proceeding cautiously.

"I wanted to take a moment to explain why we're growing the system slowly," Besbris said. "First, we want to make sure our infrastructure scales so the service remains fast and reliable. Second, we want to ensure that bugs are fixed while there are still a relatively few people in the field trial."

Google has made a couple tweaks--shutting down the ability to publicly share an initially private post last week, for one thing. Another change came yesterday involving profile pictures. "Changing your public profile picture or scrapbook photos will no longer generate a public post to the stream, just to the people you have in your circles. So only people in your circles will engage in discussions about the photos you post," Google+ product manager Shimrit Ben-Yair said in a Google+ post.

screenshot by Stephen Shankland/CNET

1.7 million Google+ users so far?

Besbris wouldn't say how many people are using Google+ right now, but it's certainly in the thousands at least. Paul Allen, founder of Ancestry.com and president of FamilyLink.com, estimated that there were 1.7 million people on Google+ on Monday, a figure based on a statistical extrapolation from the frequency of surnames. "My model uses surname distribution data from the U.S. Census Bureau and compares it to how many Google+ users there currently are with a small sampling of surnames in the U.S. and in the world," he said of his method.

Google+ is a sprawling product, too, and it's taken time for people to grasp its many mechanisms for organizing contacts, sharing posts publicly or selectively, and figuring out details such as, say, the difference between the default stream of contacts' posts (which shows posts from people in all your circles) and the "incoming" stream (which shows posts from people who put you in one of their circles). And Google+ can be used either through a sophisticated Web app or a full-featured Android app; an iOS app for Google+ has been submitted for approval.

No wonder then that newbie guides are popping up. My favorite compendium so far is one from Andrew Shotland. I also liked this flowchart showing how comments are shared with others on Google+.

Google+'s tentacles extend well beyond Google+ itself. Google Docs notifies you of updates. E-mail invitations arrive frequently with word of new followers and discussion replies. The Google home page features a link to your Google+ page. People's Google Profile pages now anchor their Google+ identities--and in a sign that Google is serious about this social networking thing, Google will delete any profiles that aren't made public by July 31. (Here's an idea: why doesn't Google send anybody in that situation an automatic Google+ invitation to try to win them over?)

It's not clear when Google will open up the invitations again, though clearly it will. When it does, Besbris advises you proceed cautiously, too.

"We continue to throttle invites, so please don't mass invite folks as it won't work," he said. "If you invite a handful of your most important friends and family you're much more likely to get these folks into our system."

Business demand, too

Google also is wrestling with business demand for Google+--something to match Facebook pages that need not be tied to a single individual.

Business accounts will be coming later this year, Google product manager Christian Oestlian said yesterday in a Google+ post. He also noted that Google will shut down existing non-individual accounts--well, most of them at least.

"Right now we're very much focused on optimizing for the consumer experience, but we have a great team of engineers building a similarly optimized business experience for Google+. We're very excited about it and we hope to roll it out later on this year," Oestlian said in a video about the option.

Several corporations have already jumped onto Google+, but it's not "optimally suited" for them, Oestlian said, and Google is shutting them down even as it plans to test what it hopes to actually launch:

The business experience we are creating should far exceed the consumer profile in terms of its usefulness to businesses. We just ask for your patience while we build it. In the meantime, we are discouraging businesses from using regular profiles to connect with Google+ users. Our policy team will actively work with profile owners to shut down non-user profiles. Over the next few months we are going to be running a small experiment with a few marketing partners to see the effect of including brands in the Google+ experience. We'll begin this pilot with a small number of named partners.

Given that companies had already jumped aboard, it appears that at least some businesses would prefer a suboptimal experience to none at all. A measured debut is a sensible way of heading off problems before they're big, but Google also would do well to tap into the Google+ enthusiasm while it's still strong.