Inflation has slowed a lot — great. Here’s what is not so great.

The good news this week on inflation cheered Wall Street investors. Stocks rose on Thursday for the fourth day in a row,

Many economists also predicted the Federal Reserve is “one and done,” meaning it will raise interest one more time in July and call it quits.

The fight against inflation is not over by a long shot, however.

Other measures of prices seen as better predictors of future trends show inflation stuck in the 4% to 5% range, well above the Fed’s long-run goal of 2%.

The yearly increase in so-called core consumer prices — everything except food and energy — registered 4.8% in June. And the core PCE inflation rate, the Fed’s preferred gauge, stood at 4.6% in its last reading.

“It’s much easier to go from 9% to 4% inflation than from 4% to 2%,” said chief economist Richard Moody of Regions Financial. ” The hardest part is yet to come.”

A lot has been working in the Fed’s favor as it ratcheted up interest rates this year to try to tamp down high inflation.

A big runup in the cost of oil and food after last year’s Russian invasion of Ukraine has unwound, for one thing. Cheaper oil and smaller increases in food prices help to explain the big slowdown in inflation this year.

Higher interest rates orchestrated by the Fed and other central banks around the world have also slowed the global economy and reduced demand among consumers and businesses.

Less demand has allowed congested global supply lines to clear up and ease the upward pressure on prices. Widespread shortages a few years ago played a big role in the increase in inflation.

Business leaders and Fed economists have also found greater resistance lately to price increases. Consumers are balking at paying more and sometimes avoiding certain products altogether, giving companies pause.

“Contacts in some [of the Fed’s 12] districts noted reluctance to raise prices because consumers had grown more sensitive to prices,” the central bank’s Beige Book economic survey said this week.

The rate of price increases has to come down a lot further, however, to mollify senior officials at the Fed who are bent on restoring inflation to pre-pandemic levels of 2% or less.

“It is really too early to declare victory on inflation,” San Francisco Fed President Mary Daly said in an interview on CNBC. The Fed itself doesn’t see inflation falling to 2% until 2025.

Matthew Martin, U.S. economist at Oxford Economics, said the cost of housing and labor remain big sore spots.

Rent and home prices surged in 2022 and helped spur inflation to the highest level since the early 1980s. Shelter is the single biggest expense for most people.

Rents and housing costs are still running high. Rents are up 8.3% in the past year, for example.

Read: Longing for the return of pre-pandemic rents? Don’t get your hopes up.

Martin said there are signs shelter costs are cooling, but wages appear frozen at elevated levels. Average hourly pay rose 4.4% in the 12 months ended in June, leaving it unchanged since the early spring.

“The biggest issue [with inflation] is on the wage side,” he said.

What happens next? The Fed is widely expected to raise interest rates at its next meeting on July 25-26, then wait to see how much further inflation slows. The Fed has jacked up a key short-term interest rate to a top end of 5.25% from near zero a year and a half ago.

Neil Dutta, head of macroeconomics at Renaissance Macro Research, said investors should not “ring the all-clear bell just yet.”

He pointed out the housing market appears to be on the rebound, possibly limiting further slowdown in rents and home prices.

The economy is also growing fast enough to stoke demand for goods, services and labor, he said, potentially keeping inflation well above the Fed’s target.

That’s why many forecasters still think a recession is likely, even if the odds are somewhat lower. The Fed will keep the pressure on the economy — either by raising rates or keeping them high for a while — to squeeze out inflationary forces.

“People thinking we are past the worst,” Moody said. “All this means is prices are rising more slowly, but they are still rising.”