diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 5dfddb7..bc02627 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -26,6 +26,10 @@
 # on non-POSIX platforms.
 add_definitions("-D_POSIX_C_SOURCE=200809L")
 
+# If SKIP_TEST_SUITES is not defined with -D, get it from the environment.
+if((NOT DEFINED SKIP_TEST_SUITES) AND (DEFINED ENV{SKIP_TEST_SUITES}))
+    set(SKIP_TEST_SUITES $ENV{SKIP_TEST_SUITES})
+endif()
 # Test suites caught by SKIP_TEST_SUITES are built but not executed.
 # "foo" as a skip pattern skips "test_suite_foo" and "test_suite_foo.bar"
 # but not "test_suite_foobar".
diff --git a/tests/include/test/constant_flow.h b/tests/include/test/constant_flow.h
index af64011..ebd0c6a 100644
--- a/tests/include/test/constant_flow.h
+++ b/tests/include/test/constant_flow.h
@@ -50,6 +50,12 @@
  * This file contains two implementations: one based on MemorySanitizer, the
  * other on valgrind's memcheck. If none of them is enabled, dummy macros that
  * do nothing are defined for convenience.
+ *
+ * \note #TEST_CF_SECRET must be called directly from within a .function file,
+ *       not indirectly via a macro defined under tests/include or a function
+ *       under tests/src. This is because we only run Valgrind for constant
+ *       flow on test suites that have greppable annotations inside them (see
+ *       `skip_suites_without_constant_flow` in `tests/scripts/all.sh`).
  */
 
 #if defined(MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN)
diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index bb4e9b7..3426cf1 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -1555,6 +1555,17 @@
     env OPENSSL_CMD="$OPENSSL_NEXT" tests/compat.sh -e '^$' -f 'ARIA\|CHACHA'
 }
 
+skip_suites_without_constant_flow () {
+    # Skip the test suites that don't have any constant-flow annotations.
+    # This will need to be adjusted if we ever start declaring things as
+    # secret from macros or functions inside tests/include or tests/src.
+    SKIP_TEST_SUITES=$(
+        git -C tests/suites grep -L TEST_CF_ 'test_suite_*.function' |
+            sed 's/test_suite_//; s/\.function$//' |
+            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:
@@ -1586,12 +1597,13 @@
     msg "build: cmake release GCC, full config with constant flow testing"
     scripts/config.py full
     scripts/config.py set MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND
+    skip_suites_without_constant_flow
     cmake -D CMAKE_BUILD_TYPE:String=Release .
     make
 
     # this only shows a summary of the results (how many of each type)
     # details are left in Testing/<date>/DynamicAnalysis.xml
-    msg "test: main suites (valgrind + constant flow)"
+    msg "test: some suites (valgrind + constant flow)"
     make memcheck
 }
 
@@ -3189,30 +3201,43 @@
 
 component_test_valgrind () {
     msg "build: Release (clang)"
+    # default config, in particular without MBEDTLS_USE_PSA_CRYPTO
     CC=clang cmake -D CMAKE_BUILD_TYPE:String=Release .
     make
 
-    msg "test: main suites valgrind (Release)"
+    msg "test: main suites, Valgrind (default config)"
     make memcheck
 
     # Optional parts (slow; currently broken on OS X because programs don't
     # seem to receive signals under valgrind on OS X).
+    # These optional parts don't run on the CI.
     if [ "$MEMORY" -gt 0 ]; then
-        msg "test: ssl-opt.sh --memcheck (Release)"
+        msg "test: ssl-opt.sh --memcheck (default config)"
         tests/ssl-opt.sh --memcheck
     fi
 
     if [ "$MEMORY" -gt 1 ]; then
-        msg "test: compat.sh --memcheck (Release)"
+        msg "test: compat.sh --memcheck (default config)"
         tests/compat.sh --memcheck
     fi
 
     if [ "$MEMORY" -gt 0 ]; then
-        msg "test: context-info.sh --memcheck (Release)"
+        msg "test: context-info.sh --memcheck (default config)"
         tests/context-info.sh --memcheck
     fi
 }
 
+component_test_valgrind_psa () {
+    msg "build: Release, full (clang)"
+    # full config, in particular with MBEDTLS_USE_PSA_CRYPTO
+    scripts/config.py full
+    CC=clang cmake -D CMAKE_BUILD_TYPE:String=Release .
+    make
+
+    msg "test: main suites, Valgrind (full config)"
+    make memcheck
+}
+
 support_test_cmake_out_of_source () {
     distrib_id=""
     distrib_ver=""
diff --git a/tests/suites/test_suite_constant_time.data b/tests/suites/test_suite_constant_time.data
new file mode 100644
index 0000000..4504aa4
--- /dev/null
+++ b/tests/suites/test_suite_constant_time.data
@@ -0,0 +1,11 @@
+# these are the numbers we'd get with an empty plaintext and truncated HMAC
+Constant-flow memcpy from offset: small
+ssl_cf_memcpy_offset:0:5:10
+
+# we could get this with 255-bytes plaintext and untruncated SHA-256
+Constant-flow memcpy from offset: medium
+ssl_cf_memcpy_offset:0:255:32
+
+# we could get this with 255-bytes plaintext and untruncated SHA-384
+Constant-flow memcpy from offset: large
+ssl_cf_memcpy_offset:100:339:48
diff --git a/tests/suites/test_suite_constant_time.function b/tests/suites/test_suite_constant_time.function
new file mode 100644
index 0000000..a3673b7
--- /dev/null
+++ b/tests/suites/test_suite_constant_time.function
@@ -0,0 +1,49 @@
+/* BEGIN_HEADER */
+/** \file test_suite_constant_time.function
+ *
+ * Functional testing of functions in the constant_time module.
+ *
+ * The tests are instrumented with #TEST_CF_SECRET and #TEST_CF_PUBLIC
+ * (see tests/include/test/constant_flow.h) so that running the tests
+ * under MSan or Valgrind will detect a non-constant-time implementation.
+ */
+
+#include <mbedtls/constant_time.h>
+#include <constant_time_internal.h>
+#include <constant_time_invasive.h>
+
+#include <test/constant_flow.h>
+/* END_HEADER */
+
+/* BEGIN_CASE depends_on:MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC:MBEDTLS_TEST_HOOKS */
+void ssl_cf_memcpy_offset( int offset_min, int offset_max, int len )
+{
+    unsigned char *dst = NULL;
+    unsigned char *src = NULL;
+    size_t src_len = offset_max + len;
+    size_t secret;
+
+    ASSERT_ALLOC( dst, len );
+    ASSERT_ALLOC( src, src_len );
+
+    /* Fill src in a way that we can detect if we copied the right bytes */
+    mbedtls_test_rnd_std_rand( NULL, src, src_len );
+
+    for( secret = offset_min; secret <= (size_t) offset_max; secret++ )
+    {
+        mbedtls_test_set_step( (int) secret );
+
+        TEST_CF_SECRET( &secret, sizeof( secret ) );
+        mbedtls_ct_memcpy_offset( dst, src, secret,
+                                  offset_min, offset_max, len );
+        TEST_CF_PUBLIC( &secret, sizeof( secret ) );
+        TEST_CF_PUBLIC( dst, len );
+
+        ASSERT_COMPARE( dst, len, src + secret, len );
+    }
+
+exit:
+    mbedtls_free( dst );
+    mbedtls_free( src );
+}
+/* END_CASE */
diff --git a/tests/suites/test_suite_constant_time_hmac.data b/tests/suites/test_suite_constant_time_hmac.data
new file mode 100644
index 0000000..5339f20
--- /dev/null
+++ b/tests/suites/test_suite_constant_time_hmac.data
@@ -0,0 +1,15 @@
+Constant-flow HMAC: MD5
+depends_on:MBEDTLS_MD5_C
+ssl_cf_hmac:MBEDTLS_MD_MD5
+
+Constant-flow HMAC: SHA1
+depends_on:MBEDTLS_SHA1_C
+ssl_cf_hmac:MBEDTLS_MD_SHA1
+
+Constant-flow HMAC: SHA256
+depends_on:MBEDTLS_SHA256_C
+ssl_cf_hmac:MBEDTLS_MD_SHA256
+
+Constant-flow HMAC: SHA384
+depends_on:MBEDTLS_SHA512_C:!MBEDTLS_SHA512_NO_SHA384
+ssl_cf_hmac:MBEDTLS_MD_SHA384
diff --git a/tests/suites/test_suite_constant_time_hmac.function b/tests/suites/test_suite_constant_time_hmac.function
new file mode 100644
index 0000000..c19cde9
--- /dev/null
+++ b/tests/suites/test_suite_constant_time_hmac.function
@@ -0,0 +1,102 @@
+/* BEGIN_HEADER */
+
+#include <mbedtls/constant_time.h>
+#include <mbedtls/md.h>
+#include <constant_time_internal.h>
+
+#include <test/constant_flow.h>
+/* END_HEADER */
+
+/* BEGIN_CASE depends_on:MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC:MBEDTLS_TEST_HOOKS */
+void ssl_cf_hmac( int hash )
+{
+    /*
+     * Test the function mbedtls_ct_hmac() against a reference
+     * implementation.
+     */
+    mbedtls_md_context_t ctx, ref_ctx;
+    const mbedtls_md_info_t *md_info;
+    size_t out_len, block_size;
+    size_t min_in_len, in_len, max_in_len, i;
+    /* TLS additional data is 13 bytes (hence the "lucky 13" name) */
+    unsigned char add_data[13];
+    unsigned char ref_out[MBEDTLS_MD_MAX_SIZE];
+    unsigned char *data = NULL;
+    unsigned char *out = NULL;
+    unsigned char rec_num = 0;
+
+    mbedtls_md_init( &ctx );
+    mbedtls_md_init( &ref_ctx );
+
+    md_info = mbedtls_md_info_from_type( hash );
+    TEST_ASSERT( md_info != NULL );
+    out_len = mbedtls_md_get_size( md_info );
+    TEST_ASSERT( out_len != 0 );
+    block_size = hash == MBEDTLS_MD_SHA384 ? 128 : 64;
+
+    /* Use allocated out buffer to catch overwrites */
+    ASSERT_ALLOC( out, out_len );
+
+    /* Set up contexts with the given hash and a dummy key */
+    TEST_EQUAL( 0, mbedtls_md_setup( &ctx, md_info, 1 ) );
+    TEST_EQUAL( 0, mbedtls_md_setup( &ref_ctx, md_info, 1 ) );
+    memset( ref_out, 42, sizeof( ref_out ) );
+    TEST_EQUAL( 0, mbedtls_md_hmac_starts( &ctx, ref_out, out_len ) );
+    TEST_EQUAL( 0, mbedtls_md_hmac_starts( &ref_ctx, ref_out, out_len ) );
+    memset( ref_out, 0, sizeof( ref_out ) );
+
+    /*
+     * Test all possible lengths up to a point. The difference between
+     * max_in_len and min_in_len is at most 255, and make sure they both vary
+     * by at least one block size.
+     */
+    for( max_in_len = 0; max_in_len <= 255 + block_size; max_in_len++ )
+    {
+        mbedtls_test_set_step( max_in_len * 10000 );
+
+        /* Use allocated in buffer to catch overreads */
+        ASSERT_ALLOC( data, max_in_len );
+
+        min_in_len = max_in_len > 255 ? max_in_len - 255 : 0;
+        for( in_len = min_in_len; in_len <= max_in_len; in_len++ )
+        {
+            mbedtls_test_set_step( max_in_len * 10000 + in_len );
+
+            /* Set up dummy data and add_data */
+            rec_num++;
+            memset( add_data, rec_num, sizeof( add_data ) );
+            for( i = 0; i < in_len; i++ )
+                data[i] = ( i & 0xff ) ^ rec_num;
+
+            /* Get the function's result */
+            TEST_CF_SECRET( &in_len, sizeof( in_len ) );
+            TEST_EQUAL( 0, mbedtls_ct_hmac( &ctx, add_data, sizeof( add_data ),
+                                            data, in_len,
+                                            min_in_len, max_in_len,
+                                            out ) );
+            TEST_CF_PUBLIC( &in_len, sizeof( in_len ) );
+            TEST_CF_PUBLIC( out, out_len );
+
+            /* Compute the reference result */
+            TEST_EQUAL( 0, mbedtls_md_hmac_update( &ref_ctx, add_data,
+                                                   sizeof( add_data ) ) );
+            TEST_EQUAL( 0, mbedtls_md_hmac_update( &ref_ctx, data, in_len ) );
+            TEST_EQUAL( 0, mbedtls_md_hmac_finish( &ref_ctx, ref_out ) );
+            TEST_EQUAL( 0, mbedtls_md_hmac_reset( &ref_ctx ) );
+
+            /* Compare */
+            ASSERT_COMPARE( out, out_len, ref_out, out_len );
+        }
+
+        mbedtls_free( data );
+        data = NULL;
+    }
+
+exit:
+    mbedtls_md_free( &ref_ctx );
+    mbedtls_md_free( &ctx );
+
+    mbedtls_free( data );
+    mbedtls_free( out );
+}
+/* END_CASE */
diff --git a/tests/suites/test_suite_ssl.data b/tests/suites/test_suite_ssl.data
index 9b1c712..c0b76c9 100644
--- a/tests/suites/test_suite_ssl.data
+++ b/tests/suites/test_suite_ssl.data
@@ -10002,34 +10002,6 @@
 depends_on:MBEDTLS_SSL_SESSION_TICKETS:MBEDTLS_SSL_CLI_C:MBEDTLS_X509_USE_C:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECDSA_C:MBEDTLS_ECP_DP_SECP256R1_ENABLED:MBEDTLS_SHA256_C:MBEDTLS_FS_IO
 ssl_serialize_session_load_buf_size:1023:"data_files/server5.crt"
 
-Constant-flow HMAC: MD5
-depends_on:MBEDTLS_MD5_C
-ssl_cf_hmac:MBEDTLS_MD_MD5
-
-Constant-flow HMAC: SHA1
-depends_on:MBEDTLS_SHA1_C
-ssl_cf_hmac:MBEDTLS_MD_SHA1
-
-Constant-flow HMAC: SHA256
-depends_on:MBEDTLS_SHA256_C
-ssl_cf_hmac:MBEDTLS_MD_SHA256
-
-Constant-flow HMAC: SHA384
-depends_on:MBEDTLS_SHA512_C:!MBEDTLS_SHA512_NO_SHA384
-ssl_cf_hmac:MBEDTLS_MD_SHA384
-
-# these are the numbers we'd get with an empty plaintext and truncated HMAC
-Constant-flow memcpy from offset: small
-ssl_cf_memcpy_offset:0:5:10
-
-# we could get this with 255-bytes plaintext and untruncated SHA-256
-Constant-flow memcpy from offset: medium
-ssl_cf_memcpy_offset:0:255:32
-
-# we could get this with 255-bytes plaintext and untruncated SHA-384
-Constant-flow memcpy from offset: large
-ssl_cf_memcpy_offset:100:339:48
-
 Raw key agreement: nominal
 depends_on:MBEDTLS_SHA256_C
 raw_key_agreement_fail:0
diff --git a/tests/suites/test_suite_ssl.function b/tests/suites/test_suite_ssl.function
index ad95d5a..7575f78 100644
--- a/tests/suites/test_suite_ssl.function
+++ b/tests/suites/test_suite_ssl.function
@@ -4467,133 +4467,6 @@
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC:MBEDTLS_TEST_HOOKS */
-void ssl_cf_hmac( int hash )
-{
-    /*
-     * Test the function mbedtls_ct_hmac() against a reference
-     * implementation.
-     */
-    mbedtls_md_context_t ctx, ref_ctx;
-    const mbedtls_md_info_t *md_info;
-    size_t out_len, block_size;
-    size_t min_in_len, in_len, max_in_len, i;
-    /* TLS additional data is 13 bytes (hence the "lucky 13" name) */
-    unsigned char add_data[13];
-    unsigned char ref_out[MBEDTLS_MD_MAX_SIZE];
-    unsigned char *data = NULL;
-    unsigned char *out = NULL;
-    unsigned char rec_num = 0;
-
-    mbedtls_md_init( &ctx );
-    mbedtls_md_init( &ref_ctx );
-
-    md_info = mbedtls_md_info_from_type( hash );
-    TEST_ASSERT( md_info != NULL );
-    out_len = mbedtls_md_get_size( md_info );
-    TEST_ASSERT( out_len != 0 );
-    block_size = hash == MBEDTLS_MD_SHA384 ? 128 : 64;
-
-    /* Use allocated out buffer to catch overwrites */
-    ASSERT_ALLOC( out, out_len );
-
-    /* Set up contexts with the given hash and a dummy key */
-    TEST_EQUAL( 0, mbedtls_md_setup( &ctx, md_info, 1 ) );
-    TEST_EQUAL( 0, mbedtls_md_setup( &ref_ctx, md_info, 1 ) );
-    memset( ref_out, 42, sizeof( ref_out ) );
-    TEST_EQUAL( 0, mbedtls_md_hmac_starts( &ctx, ref_out, out_len ) );
-    TEST_EQUAL( 0, mbedtls_md_hmac_starts( &ref_ctx, ref_out, out_len ) );
-    memset( ref_out, 0, sizeof( ref_out ) );
-
-    /*
-     * Test all possible lengths up to a point. The difference between
-     * max_in_len and min_in_len is at most 255, and make sure they both vary
-     * by at least one block size.
-     */
-    for( max_in_len = 0; max_in_len <= 255 + block_size; max_in_len++ )
-    {
-        mbedtls_test_set_step( max_in_len * 10000 );
-
-        /* Use allocated in buffer to catch overreads */
-        ASSERT_ALLOC( data, max_in_len );
-
-        min_in_len = max_in_len > 255 ? max_in_len - 255 : 0;
-        for( in_len = min_in_len; in_len <= max_in_len; in_len++ )
-        {
-            mbedtls_test_set_step( max_in_len * 10000 + in_len );
-
-            /* Set up dummy data and add_data */
-            rec_num++;
-            memset( add_data, rec_num, sizeof( add_data ) );
-            for( i = 0; i < in_len; i++ )
-                data[i] = ( i & 0xff ) ^ rec_num;
-
-            /* Get the function's result */
-            TEST_CF_SECRET( &in_len, sizeof( in_len ) );
-            TEST_EQUAL( 0, mbedtls_ct_hmac( &ctx, add_data, sizeof( add_data ),
-                                            data, in_len,
-                                            min_in_len, max_in_len,
-                                            out ) );
-            TEST_CF_PUBLIC( &in_len, sizeof( in_len ) );
-            TEST_CF_PUBLIC( out, out_len );
-
-            /* Compute the reference result */
-            TEST_EQUAL( 0, mbedtls_md_hmac_update( &ref_ctx, add_data,
-                                                   sizeof( add_data ) ) );
-            TEST_EQUAL( 0, mbedtls_md_hmac_update( &ref_ctx, data, in_len ) );
-            TEST_EQUAL( 0, mbedtls_md_hmac_finish( &ref_ctx, ref_out ) );
-            TEST_EQUAL( 0, mbedtls_md_hmac_reset( &ref_ctx ) );
-
-            /* Compare */
-            ASSERT_COMPARE( out, out_len, ref_out, out_len );
-        }
-
-        mbedtls_free( data );
-        data = NULL;
-    }
-
-exit:
-    mbedtls_md_free( &ref_ctx );
-    mbedtls_md_free( &ctx );
-
-    mbedtls_free( data );
-    mbedtls_free( out );
-}
-/* END_CASE */
-
-/* BEGIN_CASE depends_on:MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC:MBEDTLS_TEST_HOOKS */
-void ssl_cf_memcpy_offset( int offset_min, int offset_max, int len )
-{
-    unsigned char *dst = NULL;
-    unsigned char *src = NULL;
-    size_t src_len = offset_max + len;
-    size_t secret;
-
-    ASSERT_ALLOC( dst, len );
-    ASSERT_ALLOC( src, src_len );
-
-    /* Fill src in a way that we can detect if we copied the right bytes */
-    mbedtls_test_rnd_std_rand( NULL, src, src_len );
-
-    for( secret = offset_min; secret <= (size_t) offset_max; secret++ )
-    {
-        mbedtls_test_set_step( (int) secret );
-
-        TEST_CF_SECRET( &secret, sizeof( secret ) );
-        mbedtls_ct_memcpy_offset( dst, src, secret,
-                                  offset_min, offset_max, len );
-        TEST_CF_PUBLIC( &secret, sizeof( secret ) );
-        TEST_CF_PUBLIC( dst, len );
-
-        ASSERT_COMPARE( dst, len, src + secret, len );
-    }
-
-exit:
-    mbedtls_free( dst );
-    mbedtls_free( src );
-}
-/* END_CASE */
-
 /* BEGIN_CASE depends_on:MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED:MBEDTLS_USE_PSA_CRYPTO:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_ECP_DP_SECP256R1_ENABLED:MBEDTLS_ENTROPY_C:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_CTR_DRBG_C:MBEDTLS_ECP_C:MBEDTLS_ECDSA_C */
 void raw_key_agreement_fail( int bad_server_ecdhe_key )
 {