LEH, India — Perched high in the Himalayas, near India’s border with China, the tiny town of Leh sometimes seems as if it has been left behind by modern technology. Internet and cellphone service is spotty, the two roads to the outside world are snowed in every winter, and Buddhist monasteries compete with military outposts for prime mountaintop locations.

But early each morning, the convenience of the digital age arrives, by way of a plane carrying 15 to 20 bags of packages from Amazon. At an elevation of 11,562 feet, Leh is the highest spot in the world where the company offers speedy delivery.