diff --git a/tests/opt-testcases/tls13-compat.sh b/tests/opt-testcases/tls13-compat.sh
old mode 100755
new mode 100644
index b3a02953a2..d5e61b165c
--- a/tests/opt-testcases/tls13-compat.sh
+++ b/tests/opt-testcases/tls13-compat.sh
@@ -1,18 +1,12 @@
-#!/bin/sh
-
-# tls13-compat.sh
-#
-# Copyright The Mbed TLS Contributors
-# SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
-#
-# Purpose
-#
-# List TLS1.3 compat test cases. They are generated by
-# `./tests/scripts/generate_tls13_compat_tests.py -a -o ./tests/opt-testcases/tls13-compat.sh`.
+# TLS 1.3 interoperability test cases (equivalent of compat.sh for TLS 1.3).
+# They are generated by
+# `tests/scripts/generate_tls13_compat_tests.py -a -o ./tests/opt-testcases/tls13-compat.sh`.
 #
 # PLEASE DO NOT EDIT THIS FILE. IF NEEDED, PLEASE MODIFY `generate_tls13_compat_tests.py`
 # AND REGENERATE THIS FILE.
-#
+
+# Copyright The Mbed TLS Contributors
+# SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
 
 DATA_FILES_PATH=../framework/data_files
 requires_config_enabled MBEDTLS_SSL_SRV_C
diff --git a/tests/opt-testcases/tls13-kex-modes.sh b/tests/opt-testcases/tls13-kex-modes.sh
old mode 100755
new mode 100644
index 782bda2283..155149f1c9
--- a/tests/opt-testcases/tls13-kex-modes.sh
+++ b/tests/opt-testcases/tls13-kex-modes.sh
@@ -1,14 +1,12 @@
-#!/bin/sh
-
-# tls13-kex-modes.sh
-#
-# Copyright The Mbed TLS Contributors
-# SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
-#
+# Systematic testing of TLS 1.3 key exchange modes.
 
 # DO NOT ADD NEW TEST CASES INTO THIS FILE. The left cases will be generated by
 # scripts in future(#6280)
 
+# Copyright The Mbed TLS Contributors
+# SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
+#
+
 requires_gnutls_tls1_3
 requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C
 requires_config_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_ENABLED
diff --git a/tests/opt-testcases/tls13-misc.sh b/tests/opt-testcases/tls13-misc.sh
old mode 100755
new mode 100644
index f6520a13b0..ac91093fd2
--- a/tests/opt-testcases/tls13-misc.sh
+++ b/tests/opt-testcases/tls13-misc.sh
@@ -1,7 +1,5 @@
-#!/bin/sh
+# Miscellaneous tests of TLS 1.3 features.
 
-# tls13-misc.sh
-#
 # Copyright The Mbed TLS Contributors
 # SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
 #
diff --git a/tests/scripts/generate_tls13_compat_tests.py b/tests/scripts/generate_tls13_compat_tests.py
index dde37b765d..92ca5d623a 100755
--- a/tests/scripts/generate_tls13_compat_tests.py
+++ b/tests/scripts/generate_tls13_compat_tests.py
@@ -533,21 +533,16 @@ def generate_hrr_compat_test(client=None, server=None,
                      client_object.pre_checks() +
                      [cmd])
 
-SSL_OUTPUT_HEADER = '''#!/bin/sh
-
-# {filename}
-#
-# Copyright The Mbed TLS Contributors
-# SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
-#
-# Purpose
-#
-# List TLS1.3 compat test cases. They are generated by
+SSL_OUTPUT_HEADER = '''\
+# TLS 1.3 interoperability test cases (equivalent of compat.sh for TLS 1.3).
+# They are generated by
 # `{cmd}`.
 #
 # PLEASE DO NOT EDIT THIS FILE. IF NEEDED, PLEASE MODIFY `generate_tls13_compat_tests.py`
 # AND REGENERATE THIS FILE.
-#
+
+# Copyright The Mbed TLS Contributors
+# SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
 '''
 DATA_FILES_PATH_VAR = '''
 DATA_FILES_PATH=../framework/data_files