diff --git a/library/constant_time_impl.h b/library/constant_time_impl.h
index 35b0ee8..111b9af 100644
--- a/library/constant_time_impl.h
+++ b/library/constant_time_impl.h
@@ -48,8 +48,14 @@
     #pragma GCC diagnostic ignored "-Wredundant-decls"
 #endif
 
-/* Disable asm under Memsan because it confuses Memsan and generates false errors */
-#if defined(MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN)
+/* Disable asm under Memsan because it confuses Memsan and generates false errors.
+ *
+ * We also disable under Valgrind by default, because it's more useful
+ * for Valgrind to test the plain C implementation. MBEDTLS_TEST_CONSTANT_FLOW_ASM //no-check-names
+ * may be set to permit building asm under Valgrind.
+ */
+#if defined(MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN) || \
+    (defined(MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND) && !defined(MBEDTLS_TEST_CONSTANT_FLOW_ASM)) //no-check-names
 #define MBEDTLS_CT_NO_ASM
 #elif defined(__has_feature)
 #if __has_feature(memory_sanitizer)
diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index 2afc181..300ca1a 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -1892,6 +1892,16 @@
     export SKIP_TEST_SUITES
 }
 
+skip_all_except_given_suite () {
+    # Skip all but the given test suite
+    SKIP_TEST_SUITES=$(
+        ls -1 tests/suites/test_suite_*.function |
+        grep -v $1.function |
+         sed 's/tests.suites.test_suite_//; s/\.function$//' |
+        tr '\n' ,)
+    export SKIP_TEST_SUITES
+}
+
 component_test_memsan_constant_flow () {
     # This tests both (1) accesses to undefined memory, and (2) branches or
     # memory access depending on secret values. To distinguish between those:
@@ -1951,6 +1961,16 @@
     # details are left in Testing/<date>/DynamicAnalysis.xml
     msg "test: some suites (full minus MBEDTLS_USE_PSA_CRYPTO, valgrind + constant flow)"
     make memcheck
+
+    # Test asm path in constant time module - by default, it will test the plain C
+    # path under Valgrind or Memsan. Running only the constant_time tests is fast (<1s)
+    msg "test: valgrind asm constant_time"
+    scripts/config.py --force set MBEDTLS_TEST_CONSTANT_FLOW_ASM
+    skip_all_except_given_suite test_suite_constant_time
+    cmake -D CMAKE_BUILD_TYPE:String=Release .
+    make clean
+    make
+    make memcheck
 }
 
 component_test_valgrind_constant_flow_psa () {