diff --git a/test/tests/parallel/set3/config-overrides.bats b/test/tests/parallel/set1/config_overrides.bats
similarity index 100%
rename from test/tests/parallel/set3/config-overrides.bats
rename to test/tests/parallel/set1/config_overrides.bats
diff --git a/test/tests/parallel/set3/dovecot_inet_protocol.bats b/test/tests/parallel/set1/dovecot_inet_protocol.bats
similarity index 100%
rename from test/tests/parallel/set3/dovecot_inet_protocol.bats
rename to test/tests/parallel/set1/dovecot_inet_protocol.bats
diff --git a/test/tests/parallel/set3/dovecot-sieve.bats b/test/tests/parallel/set1/dovecot_sieve.bats
similarity index 100%
rename from test/tests/parallel/set3/dovecot-sieve.bats
rename to test/tests/parallel/set1/dovecot_sieve.bats
diff --git a/test/tests/serial/mail_fetchmail.bats b/test/tests/parallel/set1/fetchmail.bats
similarity index 100%
rename from test/tests/serial/mail_fetchmail.bats
rename to test/tests/parallel/set1/fetchmail.bats
diff --git a/test/tests/serial/mail_quotas_disabled.bats b/test/tests/parallel/set1/quotas_disabled.bats
similarity index 100%
rename from test/tests/serial/mail_quotas_disabled.bats
rename to test/tests/parallel/set1/quotas_disabled.bats
diff --git a/test/tests/serial/mail_special_use_folders.bats b/test/tests/parallel/set1/special_use_folders.bats
similarity index 100%
rename from test/tests/serial/mail_special_use_folders.bats
rename to test/tests/parallel/set1/special_use_folders.bats
diff --git a/test/tests/serial/mail_tls_dhparams.bats b/test/tests/parallel/set1/tls/dhparams.bats
similarity index 100%
rename from test/tests/serial/mail_tls_dhparams.bats
rename to test/tests/parallel/set1/tls/dhparams.bats
diff --git a/test/tests/parallel/set2/tls/tls_letsencrypt.bats b/test/tests/parallel/set1/tls/letsencrypt.bats
similarity index 100%
rename from test/tests/parallel/set2/tls/tls_letsencrypt.bats
rename to test/tests/parallel/set1/tls/letsencrypt.bats
diff --git a/test/tests/parallel/set2/tls/tls_manual.bats b/test/tests/parallel/set1/tls/manual.bats
similarity index 100%
rename from test/tests/parallel/set2/tls/tls_manual.bats
rename to test/tests/parallel/set1/tls/manual.bats
diff --git a/test/tests/parallel/set2/tls/tls_cipherlists.bats b/test/tests/parallel/set2/tls_cipherlists.bats
similarity index 100%
rename from test/tests/parallel/set2/tls/tls_cipherlists.bats
rename to test/tests/parallel/set2/tls_cipherlists.bats
diff --git a/test/tests/serial/mail_hostname.bats b/test/tests/parallel/set3/container_configuration/hostname.bats
similarity index 100%
rename from test/tests/serial/mail_hostname.bats
rename to test/tests/parallel/set3/container_configuration/hostname.bats
diff --git a/test/tests/parallel/set3/process-check-restart.bats b/test/tests/parallel/set3/container_configuration/process_check_restart.bats
similarity index 100%
rename from test/tests/parallel/set3/process-check-restart.bats
rename to test/tests/parallel/set3/container_configuration/process_check_restart.bats
diff --git a/test/tests/serial/mail_time.bats b/test/tests/parallel/set3/container_configuration/time.bats
similarity index 100%
rename from test/tests/serial/mail_time.bats
rename to test/tests/parallel/set3/container_configuration/time.bats
diff --git a/test/tests/parallel/set1/default_relay_host.bats b/test/tests/parallel/set3/mta/default_relay_host.bats
similarity index 100%
rename from test/tests/parallel/set1/default_relay_host.bats
rename to test/tests/parallel/set3/mta/default_relay_host.bats
diff --git a/test/tests/serial/mail_lmtp_ip.bats b/test/tests/parallel/set3/mta/lmtp_ip.bats
similarity index 100%
rename from test/tests/serial/mail_lmtp_ip.bats
rename to test/tests/parallel/set3/mta/lmtp_ip.bats
diff --git a/test/tests/serial/mail_privacy.bats b/test/tests/parallel/set3/mta/privacy.bats
similarity index 100%
rename from test/tests/serial/mail_privacy.bats
rename to test/tests/parallel/set3/mta/privacy.bats
diff --git a/test/tests/parallel/set3/smtp-delivery.bats b/test/tests/parallel/set3/mta/smtp_delivery.bats
similarity index 100%
rename from test/tests/parallel/set3/smtp-delivery.bats
rename to test/tests/parallel/set3/mta/smtp_delivery.bats
diff --git a/test/tests/serial/mail_smtponly.bats b/test/tests/parallel/set3/mta/smtponly.bats
similarity index 100%
rename from test/tests/serial/mail_smtponly.bats
rename to test/tests/parallel/set3/mta/smtponly.bats
diff --git a/test/tests/serial/mail_changedetector.bats b/test/tests/parallel/set3/scripts/changedetector.bats
similarity index 100%
rename from test/tests/serial/mail_changedetector.bats
rename to test/tests/parallel/set3/scripts/changedetector.bats
diff --git a/test/tests/parallel/set3/helper-functions.bats b/test/tests/parallel/set3/scripts/helper_functions.bats
similarity index 100%
rename from test/tests/parallel/set3/helper-functions.bats
rename to test/tests/parallel/set3/scripts/helper_functions.bats
diff --git a/test/tests/serial/setup-cli.bats b/test/tests/parallel/set3/scripts/setup_cli.bats
similarity index 100%
rename from test/tests/serial/setup-cli.bats
rename to test/tests/parallel/set3/scripts/setup_cli.bats
diff --git a/test/tests/serial/no_container.bats b/test/tests/serial/no_container.bats
index d9937497..16512527 100644
--- a/test/tests/serial/no_container.bats
+++ b/test/tests/serial/no_container.bats
@@ -1,9 +1,10 @@
 load "${REPOSITORY_ROOT}/test/helper/setup"
 load "${REPOSITORY_ROOT}/test/helper/common"
 
+# ! ATTENTION: Must be run in serial mode, as no existing containers should be present.
+
 # Tests the `setup.sh` companion script.
 # Only test coverage below is that the config path `-p` and image `-i` options work as intended.
-# NOTE: Must be run in serial mode, as no existing containers should be present.
 BATS_TEST_NAME_PREFIX='[No Existing Container] '
 
 function setup_file() {