Ted Cruz thinks he’s upstaged Donald Trump by naming former GOP presidential candidate Carly Fiorina as his prospective running mate. It’s a good move for a candidate desperate to maintain a sense of viability after devastating losses to Trump in the last six primaries.

Fiorina’s an outsider, a die-hard conservative, an attack dog, and a convenient foil to Hillary Clinton, who’s been discussing possible running mates also. If nothing else, Cruz’s gesture gives the fast-fading Texan a patina of presidential stature on the eve of what looks like certain ignominious defeat.

Trump pooh-poohed Cruz’s VP selection as little more than a desperate PR ploy. Can you blame him? Still, it does contain the seed of a good idea: Trump might consider a female running mate of his own.

And I have just the candidate for him: Cathy McMorris Rodgers, a five-term Republican congresswoman and the party’s highest ranking female member as well as a close ally of House speaker Paul Ryan, who’s been buddying up to Trump of late.

Never heard of Rodgers? You’re not alone. She may be one of the GOP’s best kept secrets, and given Trump’s political needs – both to win the election against Clinton, and to govern effectively, he should strongly consider her.

Trump hasn’t mentioned Rodgers or anyone else — except Sarah Palin — as possible contenders. But he’s already suggested his willingness to name a woman as his running mate, as long as she is the “right” one, he says. Judging from his various remarks, what he means by “right,” apparently, is an “experienced politician” who can help him push his legislative agenda through Congress.

Palin is not going to help him there. Neither is South Carolina governor Nikki Haley, an establishment conservative that many Republicans consider to be prime VP material, but who has no Washington experience.

Rodgers, by contrast, is the perfect choice. She’s about as close to a powerful behind-the-scenes legislative ally as Trump could find, in fact. She’s not only served on key committees like Armed Services and Energy, she’s also co-chaired the bipartisan House Women’s Caucus. That doesn’t make her a feminist – she’s staunchly pro-life – but it does give her serious “street cred” on women’s issues, everything from tougher child support enforcement to domestic violence to more federal and state funding for women’s health programs — causes that Trump himself supports.

But Rodgers’ real cachet appears to be her persistent ability to build bridges among Republicans. She did it with John Boehner, and despite his departure, she’s emerged as a close ally of Paul Ryan whose forthcoming “Contract for America” is intended to provide guidance not just to Congress but to the new GOP president, assuming one is elected. Rodgers, who retains the trust of the entire House – she chairs the House Republican conference, only the second woman to do so – is a natural to try to bridge the GOP-controlled Congress to Trump, whom many legislators remain deeply skeptical of.

Republicans – at least the party leadership — love Rodgers. So much so that even four years ago, some party insiders tried to convince Mitt Romney to put her on the GOP ticket. Since then, House leaders have avidly promoted Rodgers to appear in public fora, including the talk show circuit as well as designating her to give the GOP’s rebuttal to President Obama’s State of the Union address in 2014. She didn’t hit a home run, but she didn’t embarrass herself either – something neither Gov. Bobby Jindal nor even Florida senator Marco Rubio can claim.

Rodgers should not be underestimated. She’s got a first-rate mind, a command of policy details, and an especially strong handle on veterans’ issues, also of great concern to Trump. She’s the consummate insider credited with fashioning highly effective talking points, especially those designed to rebut the Democrats’ “war on women” attack line. At 46, she’s part of a new breed of Republican women who are rising through the ranks of the party and her conservative credentials are impeccable.

Trump has a long – and indeed admirable — history of appointing women to top positions in his organization and delegating major responsibilities to them. He could do far worse than consider putting Rodgers on the ticket – not as a way of pandering to women, who are disappointed with Clinton anyway, but as a clear sign of where he and the party stand when it comes to putting the best, most effective people forward – regardless of gender.