diff --git a/ALGORITHMS.md b/ALGORITHMS.md
index 2da4dcf0..236cef8a 100644
--- a/ALGORITHMS.md
+++ b/ALGORITHMS.md
@@ -44,11 +44,11 @@ As standardization for these algorithms within TLS is not done, all TLS code poi
 | mlkem768 | 0x0768 | Yes | OQS_CODEPOINT_MLKEM768 |
 | p384_mlkem768 | 0x2F4C | Yes | OQS_CODEPOINT_P384_MLKEM768 |
 | x448_mlkem768 | 0x2FB7 | Yes | OQS_CODEPOINT_X448_MLKEM768 |
-| x25519_mlkem768 | 4588 | Yes | OQS_CODEPOINT_X25519_MLKEM768 |
-| p256_mlkem768 | 0x2F4E | Yes | OQS_CODEPOINT_P256_MLKEM768 |
+| x25519_mlkem768 | 0x2FB8 | Yes | OQS_CODEPOINT_X25519_MLKEM768 |
+| p256_mlkem768 | 4587 | Yes | OQS_CODEPOINT_P256_MLKEM768 |
 | mlkem1024 | 0x1024 | Yes | OQS_CODEPOINT_MLKEM1024 |
 | p521_mlkem1024 | 0x2F4D | Yes | OQS_CODEPOINT_P521_MLKEM1024 |
-| p384_mlkem1024 | 0x2F4F | Yes | OQS_CODEPOINT_P384_MLKEM1024 |
+| p384_mlkem1024 | 0x2F4E | Yes | OQS_CODEPOINT_P384_MLKEM1024 |
 | bikel1 | 0x0241 | Yes | OQS_CODEPOINT_BIKEL1 |
 | p256_bikel1 | 0x2F41 | Yes | OQS_CODEPOINT_P256_BIKEL1 |
 | x25519_bikel1 | 0x2FAE | Yes | OQS_CODEPOINT_X25519_BIKEL1 |
diff --git a/oqs-template/generate.yml b/oqs-template/generate.yml
index e0e29e13..514c05e6 100644
--- a/oqs-template/generate.yml
+++ b/oqs-template/generate.yml
@@ -1,5 +1,5 @@
 # This is the master document for ID interoperability for KEM IDs, p-hybrid KEM IDs, SIG (O)IDs
-# Next free plain KEM ID: 0x024D, p-hybrid: 0x2F50, X-hybrid: 0x2FB8
+# Next free plain KEM ID: 0x024D, p-hybrid: 0x2F4F, X-hybrid: 0x2FB9
 kems:
   -
     family: 'FrodoKEM'
@@ -180,14 +180,12 @@ kems:
         - hybrid_group: "x448"
 # code point not standardized: Why? XXX
           nid: '0x2FB7'
-# https://www.ietf.org/archive/id/draft-kwiatkowski-tls-ecdhe-mlkem-01.html#name-iana-considerations
-        - hybrid_group: "x25519"
-          nid: '4588'
-# https://www.ietf.org/archive/id/draft-kwiatkowski-tls-ecdhe-mlkem-01.html#name-iana-considerations
 # To change when hybrid order change implemented, see https://github.com/open-quantum-safe/oqs-provider/issues/503
+        - hybrid_group: "x25519"
+          nid: '0x2FB8'
         - hybrid_group: "p256"
-# code point not standardized: Why? XXX
-          nid: '0x2F4E'
+# https://www.ietf.org/archive/id/draft-kwiatkowski-tls-ecdhe-mlkem-01.html#name-iana-considerations
+          nid: '4587'
   -
     family: 'ML-KEM'
     name_group: 'mlkem1024'
@@ -207,7 +205,7 @@ kems:
 # does Tresorit want to update?
           hybrid_oid: '1.3.6.1.4.1.42235.6'
 # code point not standardized: Why? XXX
-          nid: '0x2F4F'
+          nid: '0x2F4E'
   -
     family: 'BIKE'
     name_group: 'bike1l1fo'
diff --git a/oqs-template/oqs-kem-info.md b/oqs-template/oqs-kem-info.md
index 637ff6e7..db953c5b 100644
--- a/oqs-template/oqs-kem-info.md
+++ b/oqs-template/oqs-kem-info.md
@@ -87,12 +87,12 @@
 | HQC            | 2023-04-30               | hqc256         | 4            |                    5 | 0x2F46       | secp521_r1                       |
 | ML-KEM         | ML-KEM                   | mlkem1024      | FIPS203      |                    5 | 0x1024       |                                  |
 | ML-KEM         | ML-KEM                   | mlkem1024      | FIPS203      |                    5 | 0x2F4D       | secp521_r1                       |
-| ML-KEM         | ML-KEM                   | mlkem1024      | FIPS203      |                    5 | 0x2F4F       | p384                             |
+| ML-KEM         | ML-KEM                   | mlkem1024      | FIPS203      |                    5 | 0x2F4E       | p384                             |
 | ML-KEM         | ML-KEM                   | mlkem512       | FIPS203      |                    1 | 0x024A       |                                  |
 | ML-KEM         | ML-KEM                   | mlkem512       | FIPS203      |                    1 | 0x2F4B       | secp256_r1                       |
 | ML-KEM         | ML-KEM                   | mlkem512       | FIPS203      |                    1 | 0x2FB6       | x25519                           |
 | ML-KEM         | ML-KEM                   | mlkem768       | FIPS203      |                    3 | 0x0768       |                                  |
 | ML-KEM         | ML-KEM                   | mlkem768       | FIPS203      |                    3 | 0x2F4C       | secp384_r1                       |
-| ML-KEM         | ML-KEM                   | mlkem768       | FIPS203      |                    3 | 0x2F4E       | p256                             |
 | ML-KEM         | ML-KEM                   | mlkem768       | FIPS203      |                    3 | 0x2FB7       | x448                             |
-| ML-KEM         | ML-KEM                   | mlkem768       | FIPS203      |                    3 | 4588         | x25519                           |
+| ML-KEM         | ML-KEM                   | mlkem768       | FIPS203      |                    3 | 0x2FB8       | x25519                           |
+| ML-KEM         | ML-KEM                   | mlkem768       | FIPS203      |                    3 | 4587         | p256                             |
diff --git a/oqsprov/oqsprov_capabilities.c b/oqsprov/oqsprov_capabilities.c
index 39565f5d..d51631b0 100644
--- a/oqsprov/oqsprov_capabilities.c
+++ b/oqsprov/oqsprov_capabilities.c
@@ -78,12 +78,12 @@ static OQS_GROUP_CONSTANTS oqs_group_list[] = {
 
     {0x2F4C, 192, TLS1_3_VERSION, 0, -1, -1, 1},
     {0x2FB7, 192, TLS1_3_VERSION, 0, -1, -1, 1},
-    {4588, 192, TLS1_3_VERSION, 0, -1, -1, 1},
-    {0x2F4E, 192, TLS1_3_VERSION, 0, -1, -1, 1},
+    {0x2FB8, 192, TLS1_3_VERSION, 0, -1, -1, 1},
+    {4587, 192, TLS1_3_VERSION, 0, -1, -1, 1},
     {0x1024, 256, TLS1_3_VERSION, 0, -1, -1, 1},
 
     {0x2F4D, 256, TLS1_3_VERSION, 0, -1, -1, 1},
-    {0x2F4F, 256, TLS1_3_VERSION, 0, -1, -1, 1},
+    {0x2F4E, 256, TLS1_3_VERSION, 0, -1, -1, 1},
     {0x0241, 128, TLS1_3_VERSION, 0, -1, -1, 1},
 
     {0x2F41, 128, TLS1_3_VERSION, 0, -1, -1, 1},