diff --git a/tests/suites/test_suite_lms.data b/tests/suites/test_suite_lms.data
index 869153f78..7802a70e6 100644
--- a/tests/suites/test_suite_lms.data
+++ b/tests/suites/test_suite_lms.data
@@ -13,7 +13,7 @@ LMS pyhsslms interop test #1
 # limited amount of available test vectors for LMS. The private key is stored in
 # data_files/lms_pyhsslms_sha256_m32_h5_lmots_sha256_n32_w8_prv. Note that this signature
 # uses leaf key 0, so must be the first signature generated by the key if the
-# signature is to be reproduced. Message data is random. Note that hash-sigs
+# signature is to be reproduced. Message data is random. Note that pyhsslms
 # stores public keys and signatures in HSS form, which appends a 4-byte "levels"
 # word at the start of the key/sig. We strip these 4 bytes from the signature
 # and the public key before including them in a the test data.
@@ -27,42 +27,26 @@ LMS pyhsslms interop test #1
 # import pyhsslms
 #
 # private_key = pyhsslms.HssLmsPrivateKey('tmp/lms')
-#
-# message = bytes.fromhex('60da1a17c88c59da8a730e6ca8effd37')
 # public_key = private_key.hss_pub
-# sig = private_key.sign(message)
-# print('lms_verify_test:"{}":"{}":"{}":0'.format(message.hex(), sig.hex(), public_key.serialize().hex()))
-lms_verify_test:"60da1a17c88c59da8a730e6ca8effd37":"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":"000000010000000600000004d96bb26744d99ef624e32161c36d3d6efcdd0484e2b17a6dd183125be4b1af1cda931a91a3acb1151877c174f7943fd9":0
+#
+# message1 = bytes.fromhex('60da1a17c88c59da8a730e6ca8effd37')
+# sig1 = private_key.sign(message1)[4:]
+# print('lms_verify_test:"{}":"{}":"{}":0'.format(message1.hex(), sig1.hex(), public_key.serialize()[4:].hex()))
+lms_verify_test:"60da1a17c88c59da8a730e6ca8effd37":"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":"0000000600000004d96bb26744d99ef624e32161c36d3d6efcdd0484e2b17a6dd183125be4b1af1cda931a91a3acb1151877c174f7943fd9":0
 
 LMS pyhsslms interop test #2
-# This test uses data from https://github.com/russhousley/pyhsslms due to the
-# limited amount of available test vectors for LMS. The private key is stored in
-# data_files/lms_pyhsslms_sha256_m32_h5_lmots_sha256_n32_w8_prv. Note that this signature
-# uses leaf key 1, so must be the second signature generated by the key if the
-# signature is to be reproduced. Message data is random. Note that hash-sigs
-# stores public keys and signatures in HSS form, which appends a 4-byte "levels"
-# word at the start of the key/sig. We strip these 4 bytes from the signature
-# and the public key before including them in a the test data.
+# This test case continues from "LMS pyhsslms interop test #1".
+# The signature uses leaf key 1, so must be the second signature generated by
+# the key if the signature is to be reproduced.
 #
 # To produce another signature with this message and key (note that the actual
-# signature bytes will differ due to randomization):
-# * pip3 install --user pyhsslms
-# * cp data_files/lms_pyhsslms_sha256_m32_h5_lmots_sha256_n32_w8_prv tmp/lms.prv
-# * cp data_files/lms_pyhsslms_sha256_m32_h5_lmots_sha256_n32_w8_pub tmp/lms.pub
+# signature bytes will differ due to randomization), after generating the
+# first signature:
 #
-#import pyhsslms
-#
-#private_key = pyhsslms.HssLmsPrivateKey('tmp/lms')
-#
-#message = bytes.fromhex('60da1a17c88c59da8a730e6ca8effd37')
-#public_key = private_key.hss_pub
-#sig = private_key.sign(message)
-#
-#message = bytes.fromhex('92d036bde8c45b8bb5dea2a072560b1e29fc4bb7dc4549ce90bccee8a6e962a1')
-#public_key = private_key.hss_pub
-#sig = private_key.sign(message)
-#print('lms_verify_test:"{}":"{}":"{}":0'.format(message.hex(), sig.hex(), public_key.serialize().hex()))
-lms_verify_test:"92d036bde8c45b8bb5dea2a072560b1e29fc4bb7dc4549ce90bccee8a6e962a1":"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":"000000010000000600000004d96bb26744d99ef624e32161c36d3d6efcdd0484e2b17a6dd183125be4b1af1cda931a91a3acb1151877c174f7943fd9":0
+# message2 = bytes.fromhex('92d036bde8c45b8bb5dea2a072560b1e29fc4bb7dc4549ce90bccee8a6e962a1')
+# sig2 = private_key.sign(message2)[4:]
+# print('lms_verify_test:"{}":"{}":"{}":0'.format(message2.hex(), sig2.hex(), public_key.serialize()[4:].hex()))
+lms_verify_test:"92d036bde8c45b8bb5dea2a072560b1e29fc4bb7dc4549ce90bccee8a6e962a1":"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":"0000000600000004d96bb26744d99ef624e32161c36d3d6efcdd0484e2b17a6dd183125be4b1af1cda931a91a3acb1151877c174f7943fd9":0
 
 LMS pyhsslms interop NULL-message test
 # This test uses data from https://github.com/russhousley/pyhsslms due to the limited