Mysql – Dovecot handshake failure, on Postfix success

I am trying to setup a Dovecot/Postfix structure, relying on a MySQL backend. I came across a problem with SSL configuration, and it's really tearing my hair out…

Situation

Dovecot listens on port 993 (IMAPs) and 995 (POP3s). I use the following command to test the connection :

openssl s_client -connect myserver.tld:993
openssl s_client -connect myserver.tld:995

The following error occurs :

error:14077410:SSL routines:SSL23_GET_SERVER_HELLO:sslv3 alert handshake failure

I've made the same tests forcing ssl2, ssl3 and tls1, same thing. Now, when I run the same test on port 465 (SMTPs by Postfix) :

openssl s_client -connect myserver.tld:465

I get a magical 220 myserver.tld ESMTP Postfix (Debian/GNU). Wonderful. MySQL-based authentication even works ! The problem is that Dovecot cannot initiate the SSL connection properly, when Postfix can. Both services share the same configuration, Postfix even uses Dovecot authentication.

Configuration

Dovecot configuration :

ssl = required
ssl_cert = </etc/ssl/myserver/myserver.tld.crt
ssl_key = </etc/ssl/myserver/myserver.tld.key
ssl_verify_client_cert = no
ssl_protocols = !SSLv2 !SSLv3 !TLSv1
ssl_cipher_list = HIGH:!SSLv2:!SSLv3:!TLSv1.0:!aNULL:!MD5

Postfix main configuration :

smtpd_tls_cert_file = /etc/ssl/myserver/myserver.tld.crt
smtpd_tls_key_file = /etc/ssl/myserver/myserver.tld.key
smtpd_use_tls = yes
smtpd_tls_auth_only = yes
smtpd_tls_loglevel = 3
smtpd_tls_received_header = no
smtpd_tls_security_level = may
smtpd_tls_session_cache_timeout = 3600s

smtpd_sasl_type = dovecot
smtpd_sasl_path = private/auth
smtpd_sasl_auth_enable = yes

smtpd_recipient_restrictions =
        permit_sasl_authenticated,
        permit_mynetworks,
        reject_unauth_destination

Postfix master configuration :

smtp      inet  n       -       -       -       -       smtpd
smtps     inet  n       -       -       -       -       smtpd
  -o syslog_name=postfix/smtps
  -o smtpd_tls_wrappermode=yes
  -o smtpd_sasl_auth_enable=yes

The SSL certificate is self-signed, I generated it myself. Over SMTP, it looks just fine.

Logs

pop3-login: Disconnected (no auth attempts in 0 secs): user=<>, rip=xx.xx.xx.xx, lip=xx.xx.xx.xx, TLS handshaking: SSL_accept() failed: error:1408A0C1:SSL routines:SSL3_GET_CLIENT_HELLO:no shared cipher, session=<ffu9UFnxZQBtvqmF>

(I get an "unknown protocol" when trying ssl2 or tls1 with the openssl s_client utility)

Anyone knows where I made the configuration mistake for Dovecot ?