President Trump is unpopular in the United Kingdom. Fairly or unfairly, he's regarded as ill-informed, rude and petty. These attitudes have been amplified by Trump's criticism of London Mayor Sadiq Khan.

Those perceptions are a problem, because the United States-United Kingdom relationship offers special benefits to our economies, our foreign policies and our mutual security.

Fortunately, Trump has good options with which to move past recent controversies and strengthen the special relationship.

To start, Trump a . A good start here would be Trump's extension of a White House invitation to the mayors of those two cities.

Khan and Trump clearly dislike each other, and a coffee summit isn't going to change that. Yet, an outstretched hand to Khan and Mayor Andy Burnham of Manchester would allow Trump to rebuild some broken fences.

Trump wouldn't need to apologize or back away from his previously stated views. He could simply greet the two mayors and say, "I felt that it would be worth exchanging views on how to better protect our cities." Trump might, for example, invite U.S. mayors to attend the White House meeting. If nothing else, a White House summit would challenge British preconceptions as to the kind of leader Trump is. Trump would show he is capable of listening.

Second, Trump should double down on his commitment to a post-Brexit U.S.-U.K. free trade deal. This would strengthen Prime Minister Theresa May in negotiations with the European Union. It would also win the favor of Britons concerned about the economy.

There's no real cost here. Trump has already expressed support for a trade deal and, because both nations have high-value-goods based economies, it would support jobs in both nations. Trump might also enjoy this statement in that it would annoy his frenemies in France and Germany!

Third, Trump should direct the Pentagon to immediately deploy a company of the 3rd Infantry Regiment "Old Guard" to London. The Old Guard is responsible for the defense of Washington, D.C., but its primary duty is ceremonial in nature. And that's exactly where the Old Guard would come into play in London.

After all, this coming Saturday, assembled companies of the British Army's foot and horse guard regiments will parade in front of the queen. Known as "Trooping the Colour", this annual event celebrates the queen's official birthday.

But this year's occasion will be especially poignant in the context of the recent terrorist attacks in Manchester and London. Correspondingly, were an Old Guard company to march alongside the British Army, it would symbolize U.S. commitment to the special relationship. Seeing as no U.S. military unit has ever participated in Trooping the Color, it would also generate very positive reaction from the British people and establishment.

Ultimately, Trump is endowed with immense power. But he needs to realize that sometimes doing the right thing needn't mean doing the biggest or most aggressive thing. Sometimes an outstretched hand is as valuable as a passionately made argument.

And via the simple invitation, statement, and deployment ideas outlined above, Trump would make a great stride towards improving his relationship with our closest ally.