diff --git a/cyrus-imapd.service b/cyrus-imapd.service
index 9773723..26ee4e9 100644
--- a/cyrus-imapd.service
+++ b/cyrus-imapd.service
@@ -10,5 +10,11 @@ ExecStart=/usr/lib/cyrus-imapd/cyrus-master $CYRUSOPTIONS
 ExecStopPost=/usr/lib/cyrus-imapd/cyr_systemd_helper stop
 PrivateTmp=true
 
+# Cyrus may spawn many processes in normal operation.  These figures are higher
+# than the defaults, but may still need to be tuned for your local
+# configuration.
+TasksMax=2048
+LimitNOFILE=16384
+
 [Install]
 WantedBy=multi-user.target