diff --git a/.github/workflows/weekly.yml b/.github/workflows/weekly.yml
index 8fcbc049b1..cbfa2c3677 100644
--- a/.github/workflows/weekly.yml
+++ b/.github/workflows/weekly.yml
@@ -16,7 +16,7 @@ jobs:
             container: openquantumsafe/ci-ubuntu-focal-x86_64:latest
             CMAKE_ARGS: -DOQS_OPT_TARGET=generic -DCMAKE_BUILD_TYPE=Debug -DOQS_ENABLE_TEST_CONSTANT_TIME=ON
             PYTEST_ARGS: --numprocesses=auto -k 'test_constant_time'
-            SKIP_ALGS: 'SPHINCS\+-SHA*,Classic-McEliece-6(.)*'
+            SKIP_ALGS: 'SPHINCS\+-SHA*, Classic-McEliece-(.)*'
           - name: extensions
             container: openquantumsafe/ci-ubuntu-focal-x86_64:latest
             CMAKE_ARGS: -DOQS_OPT_TARGET=haswell -DCMAKE_BUILD_TYPE=Debug -DOQS_ENABLE_TEST_CONSTANT_TIME=ON
diff --git a/docs/algorithms/kem/classic_mceliece.md b/docs/algorithms/kem/classic_mceliece.md
index 2efd78ebda..737cedcbf1 100644
--- a/docs/algorithms/kem/classic_mceliece.md
+++ b/docs/algorithms/kem/classic_mceliece.md
@@ -14,6 +14,7 @@
 ## Advisories
 
 - Classic-McEliece-460896, Classic-McEliece-460896f, Classic-McEliece-6960119, and Classic-McEliece-6960119f parameter sets fail memory leak testing on x86-64 when building with ``clang`` using optimization level ``-O2`` and ``-O3``. Care is advised when using the algorithm at higher optimization levels, and any other compiler and architecture.
+- Current implementation of the algorithm may not be constant-time. Additionally, environment specific constant-time leaks may not be documented; please report potential constant-time leaks when found. 
 
 ## Parameter set summary
 
diff --git a/docs/algorithms/kem/classic_mceliece.yml b/docs/algorithms/kem/classic_mceliece.yml
index c09b364b1e..9208251b01 100644
--- a/docs/algorithms/kem/classic_mceliece.yml
+++ b/docs/algorithms/kem/classic_mceliece.yml
@@ -26,6 +26,7 @@ advisories:
   building with ``clang`` using optimization level ``-O2`` and ``-O3``. Care is advised
   when using the algorithm at higher optimization levels, and any other compiler and
   architecture.
+- Current implementation of the algorithm may not be constant-time. Additionally, environment specific constant-time leaks may not be documented; please report potential constant-time leaks when found. 
 parameter-sets:
 - name: Classic-McEliece-348864
   claimed-nist-level: 1
diff --git a/tests/constant_time/kem/issues/bike_has_no_timing_protections b/tests/constant_time/kem/issues/bike_has_no_timing_protections
deleted file mode 100644
index 83601cd748..0000000000
--- a/tests/constant_time/kem/issues/bike_has_no_timing_protections
+++ /dev/null
@@ -1,18 +0,0 @@
-{
-   The implementation of BIKE in liboqs is not constant time
-   Memcheck:Cond
-   ...
-   fun:OQS_KEM_bike*
-}
-{
-   The implementation of BIKE in liboqs is not constant time
-   Memcheck:Value1
-   ...
-   fun:OQS_KEM_bike*
-}
-{
-   The implementation of BIKE in liboqs is not constant time
-   Memcheck:Value8
-   ...
-   fun:OQS_KEM_bike*
-}
diff --git a/tests/constant_time/kem/issues/classic-mceliece-348864 b/tests/constant_time/kem/issues/classic-mceliece-348864
index c00d5f6fb3..07c1510ab1 100644
--- a/tests/constant_time/kem/issues/classic-mceliece-348864
+++ b/tests/constant_time/kem/issues/classic-mceliece-348864
@@ -134,6 +134,14 @@
    fun:PQCLEAN_MCELIECE348864_AVX2_crypto_kem_keypair
 }
 
+{
+   This implementation of Classic McEliece may not be constant time.
+   Memcheck:Value8
+   src:pk_gen.c:314
+   # fun:PQCLEAN_MCELIECE348864_AVX2_pk_gen
+   fun:PQCLEAN_MCELIECE348864_AVX2_crypto_kem_keypair
+}
+
 {
    This implementation of Classic McEliece may not be constant time.
    Memcheck:Value8
@@ -166,6 +174,22 @@
    fun:PQCLEAN_MCELIECE348864_AVX2_crypto_kem_keypair
 }
 
+{
+   This implementation of Classic McEliece may not be constant time.
+   Memcheck:Value8
+   src:pk_gen.c:322
+   # fun:PQCLEAN_MCELIECE348864_AVX2_pk_gen
+   fun:PQCLEAN_MCELIECE348864_AVX2_crypto_kem_keypair
+}
+
+{
+   This implementation of Classic McEliece may not be constant time.
+   Memcheck:Cond
+   src:pk_gen.c:322
+   # fun:PQCLEAN_MCELIECE348864_AVX2_pk_gen
+   fun:PQCLEAN_MCELIECE348864_AVX2_crypto_kem_keypair
+}
+
 {
    This implementation of Classic McEliece may not be constant time.
    Memcheck:Value8
diff --git a/tests/constant_time/kem/issues/classic-mceliece-460896 b/tests/constant_time/kem/issues/classic-mceliece-460896
index d6a33ceb47..83c9703071 100644
--- a/tests/constant_time/kem/issues/classic-mceliece-460896
+++ b/tests/constant_time/kem/issues/classic-mceliece-460896
@@ -1,3 +1,19 @@
+{
+   This implementation of Classic McEliece may not be constant time.
+   Memcheck:Value8
+   src:pk_gen.c:35
+   # fun:extract_01_masks
+   fun:PQCLEAN_MCELIECE460896_AVX2_pk_gen
+}
+
+{
+   This implementation of Classic McEliece may not be constant time.
+   Memcheck:Value8
+   src:pk_gen.c:43
+   # fun:extract_mask256
+   fun:PQCLEAN_MCELIECE460896_AVX2_pk_gen
+}
+
 {
    This implementation of Classic McEliece may not be constant time.
    Memcheck:Value8
@@ -30,6 +46,14 @@
    fun:PQCLEAN_MCELIECE460896_AVX2_crypto_kem_keypair
 }
 
+{
+   This implementation of Classic McEliece may not be constant time.
+   Memcheck:Value8
+   src:pk_gen.c:315
+   # fun:PQCLEAN_MCELIECE460896_AVX2_pk_gen
+   fun:PQCLEAN_MCELIECE460896_AVX2_crypto_kem_keypair
+}
+
 {
    This implementation of Classic McEliece may not be constant time.
    Memcheck:Cond
@@ -38,6 +62,22 @@
    fun:PQCLEAN_MCELIECE460896_AVX2_crypto_kem_keypair
 }
 
+{
+   This implementation of Classic McEliece may not be constant time.
+   Memcheck:Value8
+   src:pk_gen.c:320
+   # fun:PQCLEAN_MCELIECE460896_AVX2_pk_gen
+   fun:PQCLEAN_MCELIECE460896_AVX2_crypto_kem_keypair
+}
+
+{
+   This implementation of Classic McEliece may not be constant time.
+   Memcheck:Value8
+   src:pk_gen.c:323
+   # fun:PQCLEAN_MCELIECE460896_AVX2_pk_gen
+   fun:PQCLEAN_MCELIECE460896_AVX2_crypto_kem_keypair
+}
+
 {
    This implementation of Classic McEliece may not be constant time.
    Memcheck:Value8
diff --git a/tests/constant_time/kem/issues/classic-mceliece-6960119 b/tests/constant_time/kem/issues/classic-mceliece-6960119
index 4b0646bccc..8732052e45 100644
--- a/tests/constant_time/kem/issues/classic-mceliece-6960119
+++ b/tests/constant_time/kem/issues/classic-mceliece-6960119
@@ -62,6 +62,14 @@
    fun:PQCLEAN_MCELIECE6960119_AVX2_crypto_kem_keypair
 }
 
+{
+   This implementation of Classic McEliece may not be constant time.
+   Memcheck:Value8
+   src:pk_gen.c:326
+   # fun:PQCLEAN_MCELIECE6960119_AVX2_pk_gen
+   fun:PQCLEAN_MCELIECE6960119_AVX2_crypto_kem_keypair
+}
+
 {
    This implementation of Classic McEliece may not be constant time.
    Memcheck:Cond
diff --git a/tests/constant_time/kem/issues/classic-mceliece-8192128 b/tests/constant_time/kem/issues/classic-mceliece-8192128
index c51c58ee69..ec6da0ba8a 100644
--- a/tests/constant_time/kem/issues/classic-mceliece-8192128
+++ b/tests/constant_time/kem/issues/classic-mceliece-8192128
@@ -62,6 +62,14 @@
    fun:PQCLEAN_MCELIECE8192128_AVX2_crypto_kem_keypair
 }
 
+{
+   <insert_a_suppression_name_here>
+   Memcheck:Value8
+   src:pk_gen.c:323
+   # fun:PQCLEAN_MCELIECE8192128_AVX2_pk_gen
+   fun:PQCLEAN_MCELIECE8192128_AVX2_crypto_kem_keypair
+}
+
 {
    This implementation of Classic McEliece may not be constant time.
    Memcheck:Cond