Mitt Romney’s search for a running mate appears to have narrowed, as clues to whom Romney might select as his No. 2 begin to pile up in the media.

A campaign that prides itself on discipline had, to date, exacted tight control over the process of vetting candidates to serve at the former Massachusetts governor’s No. 2, a fact that Romney bragged on Tuesday.

"I get a kick out of some of the speculation that goes on," Romney told Sean Hannity of Fox News in an interview to air this evening. "I'm not going to comment on the process of course, but I can tell you this: only Beth Myers and I know who is being vetted."

That comment came amid new reports on Tuesday that Marco Rubio, the popular Florida Republican senator, had not been asked – yet, at least – to submit the materials typically associated with vetting a vice presidential candidate.

ABC News initially reported that Rubio wasn’t being vetted, and the Washington Post followed up with indications that Rubio hadn’t made it past an initial review by Romney’s high command.

Romney’s quip to Fox served as a knowing acknowledgement, though, of what members of the media have encountered in their search for details on the veepstakes: News is fleeting, largely because the Romney campaign’s high command keeps details on lockdown.

Even some of the most plugged in advisers to Romneyworld profess genuine ignorance of the vetting process.

Myers, Romney’s former chief of staff as governor, is leading the search for a prospective vice president. She might lack some of the skills of political figures previously tasked with her job – John McCain had power lawyer A.B. Culvahouse lead his vetting in 2008 – but Myers is described as a figure whom Romney holds in high esteem. She was selected precisely because it would mean no leaks, and because she understands Romney and his desire for an experienced vice presidential candidate who won’t overshadow the top of the ticket.

Other broad contours of the process have emerged, too. A New York Times story earlier this week floated the idea that Romney could introduce his choice in July, well before the Republican convention in August. Most presidential nominees traditionally reveal their choice of a running mate shortly before their nominating convention.

Larry Downing / Reuters

GOP candidate Mitt Romney speaks at a campaign event at the Bavarian Inn Lodge in Frankenmuth, Mich.

The Times also included a kicker paragraph that suggested that the Romney campaign might be wary of selecting Chris Christie, since the bombastic New Jersey governor might threaten to overshadow Romney.

One informal Romney adviser suggested that a candidate who’s seen his stock improve is former Minnesota Gov. Tim Pawlenty, in part because Pawlenty would do anything but overshadow Romney. A runner-up in the 2008 veepstakes, Pawlenty is said to be especially appealing to Ann Romney, who’s built a rapport with Pawlenty’s wife, Mary.

Ohio Sen. Rob Portman and Wisconsin Rep. Paul Ryan are also generally perceived as short-listers for Romney. Each of them, along with Pawlenty, joined Romney for portions of his swing-state bus tour over the last five days.

Officially, most of the Republicans thought to be candidates for the vice presidency have also declined to comment on the process.

"I won't discuss the vice presidential process, out of respect for Gov. Romney," Rubio said Tuesday on CNBC. "I know he is going to make a great choice."

That means that, until the pick is made known, observers are more likely to learn about the process through candidate attrition. Case in point: Indiana Gov. Mitch Daniels agreed to become the next president of Purdue University, removing his name from the list of candidates, though he wasn’t ever seen as Romney’s likely running mate.

The few-and-far-between details stand in contrast to the McCain campaign in 2008, which had basically broadcast publicly that the Arizona Republican wished to select his friend, the independent Democratic Sen. Joe Lieberman of Connecticut, as his running mate. With the exception of McCain’s ultimate selection of Sarah Palin as his vice presidential nominee, much about the Republican’s campaign wasn’t secret.

The Romney campaign seems determined to learn from McCain’s mistakes, maybe even to a fault. The process of vetting a vice presidential candidate can be political in its own right; look no further than a top Rubio advocate’s pushback to BuzzFeed about the Florida senator’s supposed exclusion from Romney’s short list.

But in leaking few details about their search, the Romney campaign also loses out on an opportunity to show they’ve at least made an effort to seek out various candidates whose mere consideration might be needed to placate certain corners of the party.

In particular, few women except for New Hampshire Sen. Kelly Ayotte – a freshman lawmaker from New England with only scant federal experience – are thought to be under consideration by Romney.

"I think, unfortunately, Palin poisoned the well on that," said one informal Romney adviser, fretting that any woman selected as VP would draw inevitable comparisons to the former Alaska governor. "I would guess if I were inside the Romney mind that they're worried that any woman chosen will be subjected to a higher level of scrutiny. "

But beyond Rubio, there are virtually no candidates for the vice presidential slot who would represent any diversity on the Republican ticket, a dicey proposition given Romney’s political deficits with women and Latino voters, as well as his opponent this fall: the nation’s first black president.