Good morning. Mourners remembered George Floyd. Virus data shows an encouraging trend. Let’s start with a look at police departments that have made changes.

It can often feel like nothing changes with police killings. Gruesome, high-profile cases keep coming — Eric Garner, Michael Brown, Freddie Gray, Breonna Taylor, George Floyd, now Manuel Ellis — and the annual number of killings nationwide remains at about 1,100.

In several big cities, however, things have changed. Police departments have adopted new policies, and, while problems remain, the number of shootings and deaths have fallen significantly.

It’s happened in Los Angeles, where fatal police shootings have declined in each of the last four years, down to 12 last year. It’s happened in San Francisco. And it’s happened in Baltimore, Chicago, Philadelphia and Phoenix, Samuel Sinyangwe, a data scientist and activist, writes for FiveThirtyEight. “Many of these reforms were initiated in response to protests and public outcry over high-profile deaths,” he adds.

The changes often revolve around training officers to de-escalate situations and reduce the amount of force they use. Tougher measures to get rid of violent officers also seem to help. Hiring more police officers sometimes helps as well, research shows. “Overstressed, overtired officers working too many shifts generate more complaints of excessive force,” Vox’s Matthew Yglesias notes.

The most sweeping proposals to emerge in recent days, like defunding the police, are unlikely to attract broad political support. Many Americans feel positively toward the police, as David Byler of The Washington Post points out — although there are large gaps by race.

Still, most Americans also say that the police have a racism problem, and most favor reforms, such as body cameras and outside investigations of misconduct. Drew Linzer of the polling firm Civiqs notes that support for the Black Lives Matter movement surged in recent days to almost 50 percent, “the highest it has ever been in over three years of polling.”

All of which points to some common political ground on police reform. “The problem is not that we lack a playbook for fixing the police,” a former police commissioner in Philadelphia and three other experts write for the Times Opinion section. “We have one. The problem is that we have not successfully followed the one we have.” Barack Obama posted a Twitter thread last night making similar points.

1. Remembering George Floyd

A memorial service on Thursday for George Floyd was by turns personal and political, celebrating both the life he had lived and the movement that his death has inspired. Floyd’s brother Philonise recalled playing football and eating banana-and-mayonnaise sandwiches; one of his cousins, Shareeduh Tate, said, “The thing I miss most about him is his hugs.”

In a defiant eulogy, the Rev. Al Sharpton said: “George Floyd’s story has been the story of black folks. Because ever since 401 years ago, the reason we could never be who we wanted and dreamed of being is you kept your knee on our neck.” Later, with the crowd rising, he added, “It’s time for us to stand up in George’s name and say, ‘Get your knee off our necks.’”

More developments from the protests:

• Two Buffalo police officers were suspended after a video showed them shoving a 75-year-old protester. They left him on the ground while he bled from the head. Mayor Byron Brown said the man was in serious condition.
• The Buffalo video is one of hundreds across the country that have documented violent police tactics, often in response to nonviolent protests. (Related: Wesley Morris, a Times critic-at-large, writes: “The most urgent filmmaking anybody’s doing in this country right now is by black people with camera phones.”)

2. Some good news on the virus

But the actual trend may be more encouraging. The number of tests being conducted has been rising rapidly in recent weeks — which means more virus cases are being uncovered than otherwise would have been. Another key measure is the percentage of tests that come back positive (as Nate Silver of FiveThirtyEight has argued), and it has continued to decline:

Taken together, the various measures suggest that the virus’s spread continues to slow — but only modestly and not as rapidly as in some other countries.

3. An economic burden for women

The lockdown has already created burdens for mothers. They have taken on a disproportionate share of day care, home schooling and housework, research has shown. Now the reopening of many workplaces may cause a new set of problems.

The lack of child care options — with day care centers, camps and schools closed — may force women out of the labor force to take care of their children. And even temporary time away from a job often brings permanent costs, in terms of missed promotions and opportunities, as Patricia Cohen and Tiffany Hsu of The Times explain. “The limited gains made in the past decades are at risk of being rolled back,” concluded a U.N. report on the virus’s impact on women.

Here’s what else is happening

• The Trump administration moved to weaken two major environmental protections, including on clean air.
• Many Times readers and employees criticized the Opinion section’s decision to publish an Op-Ed by Senator Tom Cotton calling for the military to crack down on “lawbreakers.” Last night, a spokeswoman for The Times said a review had found that the piece “did not meet our standards” and was the result of a “rushed editorial process.”

• Lives Lived: Hecky Powell’s South Side Chicago-style barbecue restaurant was an institution in Evanston, Ill., feeding everyone from broke college students to the Chicago Bulls. He even once advised a young Barack Obama, during his run for the Illinois Senate. Powell died on May 22 at 71.

How should parents discuss race with their children? Start early, and keep the conversation going. Talk about racial differences in positive ways. Make sure any home library has books with black protagonists.

These suggestions — and many more — come from Jessica Grose, editor of The Times’s Parenting section. She spoke with experts and wrote up a list of suggested books. She told us:

We wanted to provide information for parents who want to have conversations with their children about racism and the protests over the killing of George Floyd. We also wanted to make clear that it’s a privilege to choose to have these conversations; as many of my sources emphasized, black families are having and have been having these conversations, and reading these books.

The big takeaway here is that nonblack families don’t just need to talk about racism with their kids — they need to show their kids they are also taking action.

One comment, from Jacqueline Dougé, a pediatrician and child health advocate based in Maryland, really stuck with me: “Because of our culture, I have a heavy burden as a black mom. But if I think my kids are going to end racism alone, I’m deluded.”

Stick this sauce on everything

What is lemon goop? It is somewhere between lemon marmalade and a salty, tangy jam. Stewed lemons, sugar and sea salt are turned into what is technically a condiment, though the cookbook author Dorie Greenspan prefers to call it a “transformer” — for seafood, veggies and more.

For fans of Sally Rooney

“Exciting Times,” the debut novel by author Naoise Dolan, follows a young Irishwoman as she becomes entrenched in the lives of Hong Kong’s elite. It’s already drawing comparisons to the work of another acclaimed young Irish novelist, Sally Rooney.

Our reviewer, Xuan Juliana Wang, writes that “jealousy and obsession, love and late capitalism, sex and the internet all come whirling together in a wry and bracing tale of class and privilege.”

Watch something … timely

Our weekly suggestion from Gilbert Cruz, The Times’s Culture editor:

Next Friday, the latest Spike Lee film, “Da 5 Bloods,” will be released on Netflix. It’s about a group of black vets who go back to Vietnam on a personal mission decades after the war. (A trailer is here.) Lee is an essential American filmmaker and there’s never a bad time to go through his filmography. Until then, I strongly recommend you make time for (or rewatch) “Do the Right Thing.”

The 30-year-old film about the tensions that grow over the course of a hot day on a Brooklyn block, resulting in a terrible act of violence, has always felt vital but feels particularly urgent again. “Do the Right Thing” is simultaneously blunt and subtle — appropriate for a film that embraces duality, that makes room for the philosophies of Martin Luther King Jr. and Malcolm X, that makes its viewers both like and dislike almost everyone in it. Recently, our co-chief film critics rewatched it and declared it still a towering achievement. That’s the truth, Ruth.

Diversions

• In this week’s Modern Love, a writer navigates a new relationship while under quarantine.
• Late-night hosts had some thoughts about Trump’s response to criticism from former Defense Secretary James Mattis.

Games

Thanks for spending part of your morning with The Times. See you next week. — David

A correction: In yesterday’s newsletter we mistakenly referred to the televangelist Pat Robertson as Pat Roberts.

You can see today’s print front page here.

In today’s episode of “The Daily,” five protesters discuss what brought them out to the streets. And listen to the series finale of “Rabbit Hole,” our podcast about what becomes of our lives as we move online.

The Times is providing free access to much of our coronavirus coverage. Please consider supporting our journalism with a subscription.

Ian Prasad Philbrick and Sanam Yar contributed to The Morning. You can reach the team at themorning@nytimes.com.