WASHINGTON — The miserable flu season is winding down but not quite over yet, health officials said Wednesday, even as the government picked what it hoped would be a better vaccine recipe for next fall and winter.

If it seems early to worry about the next flu season, well, producing 140 million doses of vaccine requires starting months in advance.

It’s a process that’s part science, as researchers track what flu strains are spreading in different parts of the world to predict what may come here. And it’s part luck, as this year showed when a surprise new version of an aggressive flu strain — one that arose too late to be added to the vaccine — swamped the country.

Wednesday, advisers to the Food and Drug Administration urged the government to explore ways to improve how each year’s flu vaccine is created.

“It’s hard for me to believe that we cannot do better,” said Dr. Pedro Piedra of Baylor College of Medicine in Houston.

Meanwhile, the panel recommended that next winter’s flu vaccine be sure to include the new H3N2 strain, as influenza cases around the world suggest it’s still spreading.

The flu season peaked in January and is steadily declining but there’s still a lot of illness around the country, Dr. Lisa Grohskopf of the Centers for Disease Control and Prevention said Wednesday.

The vast majority was caused by a nasty version of Type A flu, the so-called H3N2 branch of the viral family that tends to trigger more pneumonia and other complications than other forms of influenza and is particularly risky to seniors.

This winter’s flu-related hospitalizations of people 65 and older were at their highest since the government began tracking that in 2005, Grohskopf said. And while it’s too soon to know the death toll, the CDC does closely track flu-related child deaths, now at 92, close to the yearly average of 100.

This year’s vaccine was only about 18 percent effective against H3N2.