diff --git a/.github/workflows/weekly.yml b/.github/workflows/weekly.yml
index 9d0be91f07..28b6f3ccad 100644
--- a/.github/workflows/weekly.yml
+++ b/.github/workflows/weekly.yml
@@ -16,12 +16,12 @@ jobs:
             container: openquantumsafe/ci-ubuntu-focal-x86_64:latest
             CMAKE_ARGS: -DOQS_DIST_BUILD=OFF -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-[^3](.)*'
+            SKIP_ALGS: 'SPHINCS\+-SHA(.)*s-simple,SPHINCS\+-SHAKE-(.)*,Classic-McEliece-[^3](.)*'
           - name: extensions
             container: openquantumsafe/ci-ubuntu-focal-x86_64:latest
             CMAKE_ARGS: -DOQS_DIST_BUILD=OFF -DOQS_OPT_TARGET=haswell -DCMAKE_BUILD_TYPE=Debug -DOQS_ENABLE_TEST_CONSTANT_TIME=ON
             PYTEST_ARGS: --numprocesses=auto -k 'test_constant_time'
-            SKIP_ALGS: 'SPHINCS\+-SHA*,Classic-McEliece-(.)*'
+            SKIP_ALGS: 'SPHINCS\+-SHA(.)*s-simple,SPHINCS\+-SHAKE-(.)*,Classic-McEliece-[^3](.)*'
     container:
       image: ${{ matrix.container }}
     steps:
diff --git a/docs/algorithms/sig/sphincs.yml b/docs/algorithms/sig/sphincs.yml
index fa0224c408..b5148335ab 100644
--- a/docs/algorithms/sig/sphincs.yml
+++ b/docs/algorithms/sig/sphincs.yml
@@ -47,8 +47,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA2: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -77,8 +77,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA2: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -107,8 +107,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA2: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -137,8 +137,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA2: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -167,8 +167,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA2: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -197,8 +197,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA2: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -227,8 +227,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA3: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -257,8 +257,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA3: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -287,8 +287,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA3: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -317,8 +317,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA3: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -347,8 +347,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA3: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
@@ -377,8 +377,8 @@ parameter-sets:
     supported-platforms: all
     common-crypto:
     - SHA3: liboqs
-    no-secret-dependent-branching-claimed: true
-    no-secret-dependent-branching-checked-by-valgrind: true
+    no-secret-dependent-branching-claimed: false
+    no-secret-dependent-branching-checked-by-valgrind: false
     large-stack-usage: false
   - upstream: primary-upstream
     upstream-id: avx2
diff --git a/tests/constant_time/sig/issues.json b/tests/constant_time/sig/issues.json
index 9bb7eb81c4..37dc988271 100644
--- a/tests/constant_time/sig/issues.json
+++ b/tests/constant_time/sig/issues.json
@@ -5,28 +5,28 @@
   "Dilithium5": [],
   "Falcon-1024": ["falcon"],
   "Falcon-512": ["falcon"],
-  "SPHINCS+-SHA256-128f-robust": ["sphincs"],
-  "SPHINCS+-SHA256-128f-simple": ["sphincs"],
-  "SPHINCS+-SHA256-128s-robust": ["sphincs"],
-  "SPHINCS+-SHA256-128s-simple": ["sphincs"],
-  "SPHINCS+-SHA256-192f-robust": ["sphincs"],
-  "SPHINCS+-SHA256-192f-simple": ["sphincs"],
-  "SPHINCS+-SHA256-192s-robust": ["sphincs"],
-  "SPHINCS+-SHA256-192s-simple": ["sphincs"],
-  "SPHINCS+-SHA256-256f-robust": ["sphincs"],
-  "SPHINCS+-SHA256-256f-simple": ["sphincs"],
-  "SPHINCS+-SHA256-256s-robust": ["sphincs"],
-  "SPHINCS+-SHA256-256s-simple": ["sphincs"],
-  "SPHINCS+-SHAKE256-128f-robust": ["sphincs"],
-  "SPHINCS+-SHAKE256-128f-simple": ["sphincs"],
-  "SPHINCS+-SHAKE256-128s-robust": ["sphincs"],
-  "SPHINCS+-SHAKE256-128s-simple": ["sphincs"],
-  "SPHINCS+-SHAKE256-192f-robust": ["sphincs"],
-  "SPHINCS+-SHAKE256-192f-simple": ["sphincs"],
-  "SPHINCS+-SHAKE256-192s-robust": ["sphincs"],
-  "SPHINCS+-SHAKE256-192s-simple": ["sphincs"],
-  "SPHINCS+-SHAKE256-256f-robust": ["sphincs"],
-  "SPHINCS+-SHAKE256-256f-simple": ["sphincs"],
-  "SPHINCS+-SHAKE256-256s-robust": ["sphincs"],
-  "SPHINCS+-SHAKE256-256s-simple": ["sphincs"]
+  "SPHINCS+-SHA2-128f-robust": ["sphincs"],
+  "SPHINCS+-SHA2-128f-simple": ["sphincs"],
+  "SPHINCS+-SHA2-128s-robust": ["sphincs"],
+  "SPHINCS+-SHA2-128s-simple": ["sphincs"],
+  "SPHINCS+-SHA2-192f-robust": ["sphincs"],
+  "SPHINCS+-SHA2-192f-simple": ["sphincs"],
+  "SPHINCS+-SHA2-192s-robust": ["sphincs"],
+  "SPHINCS+-SHA2-192s-simple": ["sphincs"],
+  "SPHINCS+-SHA2-256f-robust": ["sphincs"],
+  "SPHINCS+-SHA2-256f-simple": ["sphincs"],
+  "SPHINCS+-SHA2-256s-robust": ["sphincs"],
+  "SPHINCS+-SHA2-256s-simple": ["sphincs"],
+  "SPHINCS+-SHAKE-128f-robust": ["sphincs"],
+  "SPHINCS+-SHAKE-128f-simple": ["sphincs"],
+  "SPHINCS+-SHAKE-128s-robust": ["sphincs"],
+  "SPHINCS+-SHAKE-128s-simple": ["sphincs"],
+  "SPHINCS+-SHAKE-192f-robust": ["sphincs"],
+  "SPHINCS+-SHAKE-192f-simple": ["sphincs"],
+  "SPHINCS+-SHAKE-192s-robust": ["sphincs"],
+  "SPHINCS+-SHAKE-192s-simple": ["sphincs"],
+  "SPHINCS+-SHAKE-256f-robust": ["sphincs"],
+  "SPHINCS+-SHAKE-256f-simple": ["sphincs"],
+  "SPHINCS+-SHAKE-256s-robust": ["sphincs"],
+  "SPHINCS+-SHAKE-256s-simple": ["sphincs"]
 }
diff --git a/tests/constant_time/sig/issues/sphincs b/tests/constant_time/sig/issues/sphincs
index 14a18ee7a6..2a944c6c03 100644
--- a/tests/constant_time/sig/issues/sphincs
+++ b/tests/constant_time/sig/issues/sphincs
@@ -1,7 +1,28 @@
 {
-   memcpy source and destination overlap see issue 1038
-   Memcheck:Overlap
-   fun:__GI_memcpy
-   fun:gen_chain
-   fun:PQCLEAN_SPHINCS*_CLEAN_wots_*
+   This implementation of SPHINCS+ may not be constant time.
+   Memcheck:Cond
+   src:wotsx1.c:29
+   # fun:PQCLEAN_SPHINCSSHA*FSIMPLE_CLEAN_wots_gen_leafx1
+   fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_treehashx1
+   fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_merkle_sign
+   fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_crypto_sign_signature
+}
+
+{
+   This implementation of SPHINCS+ may not be constant time.
+   Memcheck:Cond
+   src:wotsx1.c:58
+   # fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_wots_gen_leafx1
+   fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_treehashx1
+   fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_merkle_sign
+   fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_crypto_sign_signature
+}
+
+{
+   This implementation of SPHINCS+ may not be constant time.
+   Memcheck:Cond
+   src:utilsx1.c:65
+   # fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_treehashx1
+   fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_*_sign
+   fun:PQCLEAN_SPHINCSSHA*SIMPLE_CLEAN_crypto_sign_signature
 }