Despite a disappointing overall Consumer Price Index (CPI) report Tuesday, the cost of putting a roof over one's head appears to be softening by some measures.

January’s CPI rose 0.3% over December — and 3.1% over the prior year in January, slightly higher than December's 0.2% month-over-month increase but a deceleration from December's 3.4% annual gain.

The shelter component of the CPI surprisingly increased 0.6% in January from the previous month, up from December’s 0.5% monthly gain. "The index for shelter continued to rise in January, increasing 0.6 percent and contributing over two-thirds of the monthly all items increase," the Bureau of Labor Statistics said Tuesday.

But on a year-to-year basis, shelter inflation slowed. It was up 6% — lower than December’s 6.2% year-over-year figure and down 10 straight months from March’s peak of 8.2%.

The CPI's shelter section includes the rent of a residence and a homeowner's equivalent rent, known as the OER. It also includes lodging and household insurance.

"Shelter rose, but it's not that it increased because of rents. It increased, mainly because of hotels and motels, which haven't been a problem over the last year, but they were a problem in January," Brad Case, chief economist at Middleburg Communities, told Yahoo Finance after the report was released.

The results, though, "signal continued strong demand for all forms of housing because the economy has been so strong," Case said. "That means rates can't come down aggressively or quickly."

In anticipation of Tuesday’s CPI report, the Federal Reserve Chairman Jerome Powell said in late January that a lower rent cost reading is "coming. It's just a question of when and how big it'll be." This comes as the cost of rentals in the US slowed last year, driven in part by rising supply amid a national surge in multifamily unit construction.

Other experts agree that housing costs will continue to head down.

Read more: How to buy a house: 13 steps to getting the keys to your new home

"We expect it to continue going down, but only slowly because of the way the data is collected… over the next several months, we expect it to go below 6%," Case said ahead of the release. "We actually expect it to go down to about 3% [by next year]."

The shelter index contributes to about a third of the CPI basket. The big increase in housing costs has pushed the CPI higher. The biggest chunk of the shelter component includes OER and rent — making up about 96% of the index.