The average rate on a 30-year fixed mortgage ticked down last week to just over 6.75%, the Mortgage Bankers Association reported Wednesday.

That seems to have caught the attention of homebuyers. The same report found that the number of mortgage applications rose from a week earlier.

But there is a big difference between applying for a mortgage and getting one.

This week, a separate report from the MBA found that credit availability fell in May to its lowest level in more than 10 years. So mortgage demand and mortgage supply are moving in different directions.

The fact that credit availability is falling is a sign that banks are being cautious about lending.

“Maybe we consider additional criteria. Maybe we only look at customers that have extra liquidity on their own balance sheet that could help them weather any storms,” said Dominik Mjartan, CEO of Optus Bank in South Carolina.

Banks like his have a few reasons to hold back, he said. For one, the economy is uncertain. And two, all those bank failures earlier this year still have a lot of banks nervous about their own deposits.

“We certainly maintain a very conservative posture when it comes to managing our liquidity, because we don’t know what the future may bring,” Mjartan said.

This is a particular issue for jumbo mortgages, which are loans bigger than roughly $700,000 or even more in higher-cost areas.

Banks have to hold those on their balance sheets, unlike smaller mortgages that banks can sell off, said Odeta Kushi, deputy chief economist at First American Financial.

So by making fewer jumbo loans, “banks can then reduce their exposure to credit risk and conserve that cash if needed,” she said.

The Mortgage Bankers Association found that standards are also tighter for conventional mortgages and even government-insured mortgages, which are common for first-time homebuyers.

“The tightening credit standards might just be a requirement for tighter credit scores or higher down payments. And that could really stretch that potential first-time homebuyer,” Kushi said. Demand for mortgages rises whenever rates dip, she said.

But rates are still relatively high. That means when people get mortgages, they might get smaller ones, said Peter Alden, CEO of Bay State Savings Bank in Massachusetts.

“What people qualify for is a little bit different than it was a couple of years ago, certainly,” Alden said. Meanwhile, he said he has a long list of people who are pre-qualified for home loans — but they still haven’t found a home to buy.