>>> "EZ" == Eli Zaretskii <eliz@gnu.org> writes:

>> 
>> And the new one emacs displays perfectly. So I conclude the old ones
>> were in iso8859-8 encoding.

> No, they were in codepage-1255.  See my other message.

Hm that is confusing. Please try the following

Open a new file and write

שלום אלי

Save it as utf8, say test.txt

Now run 

iconv -f UTF-8 -t ISO8859-8  testu8.txt > test8859.txt

Open test8859.txt in emacs and you face the same problem.

So what is the conclusion? Iconv does not work correctly?