diff --git a/ci/test/00_setup_env_native_valgrind.sh b/ci/test/00_setup_env_native_valgrind.sh
index 3cada7fbdf9..e0213dbe65f 100755
--- a/ci/test/00_setup_env_native_valgrind.sh
+++ b/ci/test/00_setup_env_native_valgrind.sh
@@ -11,11 +11,8 @@ export CONTAINER_NAME=ci_native_valgrind
 export PACKAGES="valgrind python3-zmq libevent-dev libboost-dev libzmq3-dev libsqlite3-dev"
 export USE_VALGRIND=1
 export NO_DEPENDS=1
-
-# feature_init and wallet_reorgsrestore excluded for now, see https://github.com/bitcoin/bitcoin/issues/32493
 # bind tests excluded for now, see https://github.com/bitcoin/bitcoin/issues/17765#issuecomment-602068547
-export TEST_RUNNER_EXTRA="--exclude feature_init,wallet_reorgsrestore,rpc_bind,feature_bind_extra"
-
+export TEST_RUNNER_EXTRA="--exclude rpc_bind,feature_bind_extra"
 export GOAL="install"
 # TODO enable GUI
 export BITCOIN_CONFIG="\
diff --git a/ci/test/wrap-valgrind.sh b/ci/test/wrap-valgrind.sh
index 27754831848..e351cf24839 100755
--- a/ci/test/wrap-valgrind.sh
+++ b/ci/test/wrap-valgrind.sh
@@ -1,6 +1,6 @@
 #!/usr/bin/env bash
 #
-# Copyright (c) 2018-2021 The Bitcoin Core developers
+# Copyright (c) 2018-present The Bitcoin Core developers
 # Distributed under the MIT software license, see the accompanying
 # file COPYING or http://www.opensource.org/licenses/mit-license.php.
 
@@ -12,7 +12,7 @@ for b_name in "${BASE_OUTDIR}/bin"/*; do
       echo "Wrap $b ..."
       mv "$b" "${b}_orig"
       echo '#!/usr/bin/env bash' > "$b"
-      echo "valgrind --gen-suppressions=all --quiet --error-exitcode=1 --suppressions=${BASE_ROOT_DIR}/contrib/valgrind.supp \"${b}_orig\" \"\$@\"" >> "$b"
+      echo "exec valgrind --gen-suppressions=all --quiet --error-exitcode=1 --suppressions=${BASE_ROOT_DIR}/contrib/valgrind.supp \"${b}_orig\" \"\$@\"" >> "$b"
       chmod +x "$b"
     done
 done