I spent two hours walking around Arlington National Cemetery in a chilly drizzle this morning, and I could only think I should have done that sooner.

The occasion was Wreaths Across America, a relatively new tradition of placing wreaths on graves at military cemeteries. I was all set to forget about it until it had begun once again, but a tweet from ArlNow two weeks ago reminded me that I could sign up to volunteer. I filled out a form online and got an e-mail confirming my registration, which led to me waking up early this morning to take a short bikeshare ride over to Arlington’s Ord & Weitzel gate and join a line to get through a security screening.

After 35 minutes, an inspection of my bag, and a soldier’s once-over of me with a handheld metal detector, I walked into the cemetery and over to the closest truck distributing wreaths. (Yes, registering online was not actually necessary.) Another volunteer handed me a wreath, which I took over to the nearest row of graves and placed against one after reading the short story of service carved into it: name, rank, military branch, war or wars, dates of birth and death. Then I repeated the task.

We didn’t get much direction besides encouragements to say the name on each grave and the occasional unexplained instruction to skip those with a Star of David. Because I had not thought seriously before about the protocol of decorating strangers’ burial sites, I did not know that Jewish custom frowns on leaving flowers at a grave. Should I do this next year, I may bring some pebbles to place on those headstones instead.

(The tradition of leaving stones on a grave has spread to non-Jewish burial sites at Arlington; Medgar Evers’ headstone, for example, was topped with pebbles left by passerby.)

I quickly realized that two things about a headstone would catch my attention: a connection to someplace I’ve lived, or a date of death suggesting the person didn’t make it home from a war. I made a point of leaving wreaths on headstones of several people from New Jersey, D.C. and Virginia who had apparently died in Vietnam.

After half an hour, I decided to hike over to Section 60, the last resting place of those who served in Afghanistan and Iraq. The marble headstones are brighter there, the names and the religious emblems on them more diverse, the mementos left more numerous and personal. I could not avoid thinking that in an alternative universe, one or both of my cousins who fought with the Marine Corps in Iraq would be there–but unlike some of their comrades, they came home physically intact. You can’t not think of the cost of war when visiting Arlington National Cemetery, but that price exists in its rawest, most painful form in Section 60.

Volunteering at Wreaths Across America (run by a non-profit organization that has bought its wreaths from a single company with family ties) isn’t necessary to make this pilgrimage to Arlington and contemplate how much we ask of service members and their families. But it looks like I needed that push.

By 10 a.m., I was starting to have trouble finding undecorated graves. That’s when a volunteer at a truck handed me not one or two wreaths but six, and I had to walk about half a mile to find places for them. I should have taken a moment beforehand to check the @ArlingtonNatl Twitter account, which posted updates about which sections still needed wreaths.

After two hours, I could see no more headstones in need of a wreath anywhere near me. That seemed improbable, given the enormous size of Arlington–easy to overlook when you drive or bike around it, not so much when you walk more than three miles through it. But we had somehow done it. Also improbable: that after hundreds of thousands of internments at Arlington, space still exists for more. I wish I were not so convinced that we will fill it all.