diff --git a/cmdeploy/src/cmdeploy/postfix/main.cf.j2 b/cmdeploy/src/cmdeploy/postfix/main.cf.j2
index 6f88277c..9ec9f039 100644
--- a/cmdeploy/src/cmdeploy/postfix/main.cf.j2
+++ b/cmdeploy/src/cmdeploy/postfix/main.cf.j2
@@ -102,6 +102,18 @@ smtpd_peername_lookup = no
 # so instead this is handled in filtermail.
 # We use LMTP instead SMTP so we can communicate per-recipient errors back to postfix.
 default_transport = lmtp-filtermail:inet:[127.0.0.1]:{{ config.filtermail_lmtp_port_transport }}
+
+# All deliveries over lmtp-filtermail are treated
+# as having the same destination [127.0.0.1],
+# so it is not possible to limit per-destination concurrency here,
+# it is a job for filtermail-transport.
+# Total number of parallel deliveries is limited
+# by "maxproc" column in /etc/postfix/master.cf for lmtp-filtermail.
+# Settings below are to prevent Postfix queue manager
+# from limiting the number of LMTP connections to filtermail-transport.
+# Read <https://www.postfix.org/TUNING_README.html#rope> and
+# <https://www.postfix.org/SCHEDULER_README.html> for the details
+# of the Postfix algorithm that we effectively disable here.
 lmtp-filtermail_initial_destination_concurrency=10000
 lmtp-filtermail_destination_concurrency_limit=10000
 
diff --git a/cmdeploy/src/cmdeploy/postfix/master.cf.j2 b/cmdeploy/src/cmdeploy/postfix/master.cf.j2
index 84c17413..f704c96c 100644
--- a/cmdeploy/src/cmdeploy/postfix/master.cf.j2
+++ b/cmdeploy/src/cmdeploy/postfix/master.cf.j2
@@ -105,7 +105,15 @@ filter    unix -        n       n       -       -       lmtp
 authclean unix  n       -       -       -       0       cleanup
   -o header_checks=regexp:/etc/postfix/submission_header_cleanup
 
-lmtp-filtermail unix  -       -       y       -       10000       lmtp
+# Reducing `maxproc` here may result in a head of line blocking
+# when there are many messages sent to unreachable destinations
+# at the same time.
+# LMTP clients here talk to filtermail-transport.
+# LMTP has no pipelining,
+# so while filtermail-transport tries to deliver the message,
+# possibly waiting for a long connection timeout
+# or talking to a slow server, LMTP client cannot be reused.
+lmtp-filtermail unix  -       -       y       -       1000       lmtp
   -o syslog_name=postfix/lmtp-filtermail
   -o lmtp_header_checks=
   -o lmtp_tls_security_level=none