In the long list of commonly used chemicals that corrode the Great Barrier Reef, the Haereticus Environmental Laboratory highlights 13 that are commonly found in hair-and-beauty products. Alexandra Keating, daughter of a former prime minister of Australia, avoids all the chemicals on the list—not just the short version—for her new body-care company, Uni. An order of soap, shampoo, conditioner, or serum comes in two parts: a sleek dispenser shell to be re-used, and a product bottle to be swapped as you run out. Designed by Marc Atlan—the creative director behind packaging for Comme des Garçons, Dior, and Helmut Lang perfumes—the look is minimal. Plus, they’ve replaced silicone and sulfates with red algae and plum in the hair- and skin-care products. (weareuni.com) —Jensen Davis

Some unfortunate news: frigid weather will persist along the Eastern Seaboard for six more weeks. If you can no longer stomach the look of the outerwear that’s been working terribly hard for you since October, we don’t blame you. But it’s not too late to switch things up. We’ll be waiting for spring in this stretch-crêpe coat from Proenza Schouler. It’s cut in an elegant princess shape, and the off-kilter buttons provide an edge. Grace Kelly or Tippi Hedren could have worn it in an Alfred Hitchcock film. Thanks to its versatile fabric, it’s just the thing to wear as we slowly head into warmer months. Imagine it over a strappy little cocktail dress, worn out to dinner downtown on a temperate evening in April. ($2,690; net-a-porter.com) —Ashley Baker

There’s only one small problem with Tiina the Store, a meticulously edited boutique in Amagansett, New York: just about everything in there is breathtakingly expensive. But it’s for good reason. Founder Tiina Laakkonen scours the globe to source quality clothing, accessories, jewelry, and home goods that are up to her exacting standards—and won’t leave customers with even a tinge of regret. Sounds excessively optimistic, but the purchases your Air Mail style correspondent has made there through the years have proven to be smart investments. Our latest find is this hand-painted shawl by Alonpi, an artisanal Italian brand that combines the latest cashmere technology with craftsmanship traditions from Biella, Italy. Look closely to see how the gray check fabric peeks through layers of blue and brown ombré. Appearance aside, it’s so warm, cuddly, and life-affirming that it’s been going with us everywhere—from wandering around town to hanging out on the sofa and yakking it up over Zoom. ($760, tiinathestore.com) —Ashley Baker

After trying several running apps, I settled on Map My Run because it’s simple. At the start of your run, you press a neon-green “Start Workout!” button. Then, every mile, a monotone female voice—one that doesn’t pretend to inflect like a real human—dryly announces your distance, your pace, and your split time (the speed of your most recent mile), and then lets you get back to it. At the end, you’ll receive a map with your route traced in bright red, as if a kindergartner had taken a crayon to it. It’s refreshing when a fitness app is indifferent to your effort. (apps.apple.com) —Jensen Davis

In 2014, a letter claiming that Islamic extremists were secretly taking over schools in Birmingham, England, was sent to a local city councillor. The conspiracy, dubbed “Operation Trojan Horse,” sent shock waves and ignited paranoia throughout the United Kingdom. The Department of Education changed its curriculum to focus on “British values,” and several Birmingham teachers were fired or banned from the school system. After the government launched several investigations, and hundreds of similar plots were reported to the Birmingham City Council, little evidence of such a plan was found. Was the whole thing a hoax? That’s the question at the center of The New York Times and Serial Productions’s new investigative podcast, The Trojan Horse Affair. Hosts Hamza Syed, a doctor turned journalist, and Brian Reed, co-creator of the beloved podcast S-Town, look at the letter’s impact on English life and try to get to the bottom of who wrote it. (podcasts.apple.com) —Jacob Robbins

When a defense attorney claims that prosecutors send innocent people to death row, it’s tempting to dismiss the argument as one-sided. But David S. Rudolf, who has made a career of defending the wrongly convicted, makes a highly persuasive case in his bracing new book, American Injustice: Inside Stories from the Underbelly of the Criminal Justice System. Rudolf famously played a key role in overturning the conviction of the novelist Michael Peterson for the 2001 murder of his wife. (The case inspired a Netflix documentary series, The Staircase.) In this book, Rudolf recounts a number of his lesser-known but even more harrowing cases, including the story of Ray Finch, a Black man in Wilson County, North Carolina, who spent 43 years in prison for the murder of a convenience-store owner. By the time Rudolf and the Duke Law Innocence Project finally got Finch freed, the client was 83. Defense lawyers have to be persuasive and, above all, persistent. Rudolf shows just how much of both it can take to get justice. (harpercollins.com) —Alessandra Stanley