A woman in the Andes town of Villa de Leyva on the Andes Mountains in Colombia Devasahayam Chandra Dhas | E+ | Getty Images

Most stories about Americans and retirement contain words like "crisis," "poverty" and "horror." Not this one. While many people are still not saving enough for their golden years, many of them are getting better at doing so — and hopeful signs abound. Today, American households headed by individuals between the ages of 35 and 64 are running $3.83 trillion short of the amount they need to safely carry them through their post-working life, according to new data by the Employee Benefit Research Institute. However, the last time EBRI ran the numbers, in 2014, those families were $4.44 trillion behind. "That's significantly lower than it was," said Jack VanDerhei, research director at the Institute.

Across all generations, the savings shortfalls have narrowed. People between the ages of 45 and 49 are currently $43,000 behind on their retirement savings, compared with $49,740 in 2014. People in their late 30s are now $49,182 behind where they should be, instead of $63,407. "Every group under age 60 is better than they were five years ago," VanDerhei said. (EBRI uses a complex model on U.S. households to arrive at these numbers, analyzing the behavior of some 50 million retirement participants and simulating more than 1,000 different life outcomes for each retiree.) The movement at companies to auto-enroll employees in their 401(k) plans is driving much of the improvements, VanDerhei said. The stock market rally has also helped.