We now have more details and better projections on the European-bank stress test and on which banks are likely to fail the test.

The smaller-than-expected demand -- just $162 billion -- for three-month loans from the European Central Bank shows, I think, that the European banking sector is in better shape, as a whole, than initially feared. (For more on why this smaller draw is positive news, see this post.)

But the fact that some banks felt the need to grab up roughly $140 billion in six-day money yesterday, July 1, shows that some banks are still having trouble raising money in the financial markets. Analysts estimate that roughly 170 banks in Europe (out of 1,100) are having trouble accessing the markets for capital.

Which banks are still shut out of the financial markets? A big chunk is likely to be Germany's Landesbanks and Spain's cajas. (For more on Germany's Landesbanks, see this post, and for more on Spain's cajas, see this post.)

And how big are the cash calls likely to be from the banks that fail the stress test?

Estimates now say that about 20 banks will fail the test and will need to raise about $37 billion in additional capital. Public sector banks -- that is, banks with government ownership stakes such as Germany's Landesbanks -- would account for about two-thirds of the capital that needs to be raised. Private-sector banks would account for the other third.

Specific names mentioned by bankers and analysts, the Financial Times reported today, include Italy's Monte dei Paschi and Banca Popolare di Milano, and Spain's Banco Popular. Banks and analysts also fingered Greece, Portugal and Ireland as countries with banks that are likely to need to raise capital.

Public release of stress-test results, by the way, have been postponed a week until July 23.

Jim Jubak doesn't own shares of any company mentioned in this post.