diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index 717b880..1af03ad 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -2235,18 +2235,10 @@
     scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_STREAM_CIPHER
     scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_ECB_NO_PADDING
 
-    loc_accel_flags=$( echo "$loc_accel_list" | sed 's/[^ ]* */-DLIBTESTDRIVER1_MBEDTLS_PSA_ACCEL_&/g' )
-    # SHA-1 and all variants of SHA-2 are needed for ECDSA and X.509 tests.
-    # Note = we are NOT adding these ALG_SHA_xxx to the "loc_accel_flags" list
-    #       because that list is used to define accelerated components both on
-    #       the driver and main library sides. Now, albeit we need SHA_xxx to be
-    #       available on the driver side (ex: hash-and-sign algorithms), we do
-    #       not want the main library to use such accelerators.
-    loc_accel_flags="$loc_accel_flags -DLIBTESTDRIVER1_MBEDTLS_PSA_ACCEL_ALG_SHA_1"
-    loc_accel_flags="$loc_accel_flags -DLIBTESTDRIVER1_MBEDTLS_PSA_ACCEL_ALG_SHA_224"
-    loc_accel_flags="$loc_accel_flags -DLIBTESTDRIVER1_MBEDTLS_PSA_ACCEL_ALG_SHA_256"
-    loc_accel_flags="$loc_accel_flags -DLIBTESTDRIVER1_MBEDTLS_PSA_ACCEL_ALG_SHA_384"
-    loc_accel_flags="$loc_accel_flags -DLIBTESTDRIVER1_MBEDTLS_PSA_ACCEL_ALG_SHA_512"
+    # Things we wanted supported in libtestdriver1, but not accelerated in the main library:
+    # SHA-1 and all SHA-2 variants, as they are used by ECDSA deterministic.
+    loc_extra_list="ALG_SHA1 ALG_SHA_224 ALG_SHA_256 ALG_SHA_384 ALG_SHA_512"
+    loc_accel_flags=$( echo "$loc_accel_list $loc_extra_list" | sed 's/[^ ]* */-DLIBTESTDRIVER1_MBEDTLS_PSA_ACCEL_&/g' )
     make -C tests libtestdriver1.a CFLAGS="$ASAN_CFLAGS $loc_accel_flags" LDFLAGS="$ASAN_CFLAGS"
 
     # Configure and build the main libraries with drivers enabled