SMTP session:
================================8<=======================
[***@mailrelay.ourdomain.com /]# telnet 0 25
Trying 0.0.0.0...
Connected to 0.
Escape character is '^]'.
220 mailrelay.ourdomain.com ESMTP Postfix
EHLO localhost
250-mailrelay.ourdomain.com
250-PIPELINING
250-SIZE 10240000
250-VRFY
250-ETRN
250-ENHANCEDSTATUSCODES
250-8BITMIME
250 DSN
MAIL FROM: <***@ourdomain.com>
250 2.1.0 Ok
RCPT TO: <***@gmail.com>
250 2.1.5 Ok
DATA
354 End data with <CR><LF>.<CR><LF>
To: <***@gmail.com>
From: <***@ourdomain.com>

.
250 2.0.0 Ok: queued as 480582C8822
================================8<=======================

Postfix log:
================================8<=======================
2012-08-17T17:14:00.026839+04:00 mailrelay postfix/smtpd[22226]:
connect from localhost.localdomain[127.0.0.1]
2012-08-17T17:14:12.295149+04:00 mailrelay postfix/smtpd[22226]:
480582C8822: client=localhost.localdomain[127.0.0.1]
2012-08-17T17:14:19.177684+04:00 mailrelay postfix/cleanup[22399]:
480582C8822: message-id=<***@mailrelay.ourdomain.com>
2012-08-17T17:14:19.177845+04:00 mailrelay dkim-filter[1425]:
(unknown-jobid) mode select: signing
2012-08-17T17:14:19.183373+04:00 mailrelay dkim-filter[1425]:
480582C8822 "DKIM-Signature" header added
2012-08-17T17:14:19.193229+04:00 mailrelay postfix/qmgr[19619]:
480582C8822: from=<***@ourdomain.com>, size=200, nrcpt=1 (queue
active)
2012-08-17T17:14:19.428857+04:00 mailrelay postfix/smtp[22308]:
480582C8822: to=<***@gmail.com>,
relay=gmail-smtp-in.l.google.com[173.194.70.27]:25, delay=9.7,
delays=9.4/0/0.04/0.19, dsn=2.0.0, status=sent (250 2.0.0 OK
9201917281 wd2si12002916oiq.90)
2012-08-17T17:14:19.428994+04:00 mailrelay postfix/qmgr[19619]:
480582C8822: removed
================================8<=======================


dkim-milter config and keys definition:
# cat /etc/mail/dkim-milter/dkim-filter.conf | egrep -v '^$'| egrep -v '^#'
================================8<=======================
AutoRestart yes
Canonicalization relaxed/simple
InternalHosts /etc/postfix/mynetworks
KeyList /etc/mail/dkim-milter/keys/keylist
LogWhy yes
SignatureAlgorithm rsa-sha256
Syslog yes
SyslogSuccess yes
UMask 007
UserID dkim-milter
================================8<=======================

# cat /etc/mail/dkim-milter/keys/keylist
================================8<=======================
# sender-pattern:signing-domain:keypath
# *:example.com:selector
*@ourdomain.com:ourdomain.com:/etc/mail/dkim-milter/keys/climail
*@list.ourdomain.com:list.ourdomain.com:/etc/mail/dkim-milter/keys/list
*@daily.ourdomain.com:daily.ourdomain.com:/etc/mail/dkim-milter/keys/daily
================================8<=======================

Somebody known how to fix my problem?

P.S. Some software send emails only as described in Case 2 and I
cannot fix this problem in this software.