Economists had expected the services index to continue the decline that began in August as the economic fallout from the Delta variant worsened. Some other indicators had suggested as much, and indeed IHS Markit on Tuesday reported that its separate services index slipped to 54.9 in September from 55.1 in August.

Even that IHS Markit number counted as good news because an earlier “flash” estimate was lower. The implication is that survey responses that came in later in the month were more upbeat. In other words, things got better.

Considering what was going on with the pandemic, maybe that isn’t entirely surprising: In the first week of September, U.S. Covid-19 cases were near their summer peak, with an average of 145,840 new cases daily, according to the Centers for Disease Control and Prevention. In the month’s final week, that figure fell to 105,354. Still, the speed with which service-sector growth appears to have picked up is cheering. It wasn’t clear until later in the month that the decline in Covid-19 cases wasn’t just a head fake. Moreover, one might think that many activities that typically entail a bit of planning, such as business trips, would have taken a while to respond to better news on the pandemic.

If Covid-19 cases can keep falling this time, then the service sector ought to be able to grow solidly and help the economy actually achieve a full recovery. It certainly isn’t there yet: Even though gross domestic product surpassed its pre-pandemic level in the second quarter, consumer spending on services was well short of that mark.

Still, how the service sector fares in the months ahead may hinge as much on how we have changed the way we do things as how the fight against the pandemic is going. Even if case counts fall drastically, many people might still be slow to visit offices every day, for example, which will keep weighing on how many downtown services businesses fare. Having learned how to meet remotely, many business trips that occurred before the pandemic now seem nonsensical. There may also be a new seasonality that will persist for many services businesses, such as restaurants, with more activity in warmer months versus colder months than there used to be.

The service sector can keep coming back, but it still won’t be the same.

Write to Justin Lahart at justin.lahart@wsj.com