diff --git a/tests/binary-cache.sh b/tests/binary-cache.sh
index eb58ae7c1..774a260a9 100644
--- a/tests/binary-cache.sh
+++ b/tests/binary-cache.sh
@@ -1,5 +1,7 @@
 source common.sh
 
+needLocalStore "“--no-require-sigs” can’t be used with the daemon"
+
 clearStore
 clearCache
 
diff --git a/tests/check.sh b/tests/check.sh
index bc23a6634..6f985984c 100644
--- a/tests/check.sh
+++ b/tests/check.sh
@@ -1,5 +1,8 @@
 source common.sh
 
+# XXX: This shouldn’t be, but #4813 cause this test to fail
+buggyNeedLocalStore "see #4813"
+
 clearStore
 
 nix-build dependencies.nix --no-out-link
diff --git a/tests/common.sh.in b/tests/common.sh.in
index cdb84f4da..27271135f 100644
--- a/tests/common.sh.in
+++ b/tests/common.sh.in
@@ -1,5 +1,9 @@
 set -e
 
+if [[ -z "$COMMON_SH_SOURCED" ]]; then
+
+COMMON_SH_SOURCED=1
+
 export TEST_ROOT=$(realpath ${TMPDIR:-/tmp}/nix-test)/${TEST_NAME:-default}
 export NIX_STORE_DIR
 if ! NIX_STORE_DIR=$(readlink -f $TEST_ROOT/store 2> /dev/null); then
@@ -43,6 +47,9 @@ export HAVE_SODIUM="@HAVE_SODIUM@"
 export version=@PACKAGE_VERSION@
 export system=@system@
 
+export IMPURE_VAR1=foo
+export IMPURE_VAR2=bar
+
 cacheDir=$TEST_ROOT/binary-cache
 
 readLink() {
@@ -73,6 +80,10 @@ clearCacheCache() {
 }
 
 startDaemon() {
+    # Don’t start the daemon twice, as this would just make it loop indefinitely
+    if [[ "$NIX_REMOTE" == daemon ]]; then
+      return
+    fi
     # Start the daemon, wait for the socket to appear.  !!!
     # ‘nix-daemon’ should have an option to fork into the background.
     rm -f $NIX_STATE_DIR/daemon-socket/socket
@@ -82,20 +93,44 @@ startDaemon() {
         sleep 1
     done
     pidDaemon=$!
-    trap "kill -9 $pidDaemon" EXIT
+    trap "killDaemon" EXIT
     export NIX_REMOTE=daemon
 }
 
 killDaemon() {
-    kill -9 $pidDaemon
+    kill $pidDaemon
+    for i in {0.10}; do
+        kill -0 $pidDaemon || break
+        sleep 1
+    done
+    kill -9 $pidDaemon || true
     wait $pidDaemon || true
     trap "" EXIT
 }
 
+restartDaemon() {
+  [[ -z "${pidDaemon:-}" ]] && return 0
+
+  killDaemon
+  unset NIX_REMOTE
+  startDaemon
+}
+
 if [[ $(uname) == Linux ]] && [[ -L /proc/self/ns/user ]] && unshare --user true; then
     _canUseSandbox=1
 fi
 
+isDaemonNewer () {
+  [[ -n "${NIX_DAEMON_PACKAGE:-}" ]] || return 0
+  local requiredVersion="$1"
+  local daemonVersion=$($NIX_DAEMON_PACKAGE/bin/nix-daemon --version | cut -d' ' -f3)
+  return [[ $(nix eval --expr "builtins.compareVersions ''$daemonVersion'' ''2.4''") -ge 0 ]]
+}
+
+requireDaemonNewerThan () {
+  isDaemonNewer "$1" || exit 99
+}
+
 canUseSandbox() {
     if [[ ! $_canUseSandbox ]]; then
         echo "Sandboxing not supported, skipping this test..."
@@ -121,4 +156,22 @@ expect() {
     [[ $res -eq $expected ]]
 }
 
+needLocalStore() {
+  if [[ "$NIX_REMOTE" == "daemon" ]]; then
+    echo "Can’t run through the daemon ($1), skipping this test..."
+    return 99
+  fi
+}
+
+# Just to make it easy to find which tests should be fixed
+buggyNeedLocalStore () {
+  needLocalStore
+}
+
 set -x
+
+if [[ -n "${NIX_DAEMON_PACKAGE:-}" ]]; then
+    startDaemon
+fi
+
+fi # COMMON_SH_SOURCED
diff --git a/tests/dump-db.sh b/tests/dump-db.sh
index d6eea42aa..48647f403 100644
--- a/tests/dump-db.sh
+++ b/tests/dump-db.sh
@@ -1,5 +1,7 @@
 source common.sh
 
+needLocalStore "--dump-db requires a local store"
+
 clearStore
 
 path=$(nix-build dependencies.nix -o $TEST_ROOT/result)
diff --git a/tests/fixed.sh b/tests/fixed.sh
index 8f51403a7..90c4c8c32 100644
--- a/tests/fixed.sh
+++ b/tests/fixed.sh
@@ -2,9 +2,6 @@ source common.sh
 
 clearStore
 
-export IMPURE_VAR1=foo
-export IMPURE_VAR2=bar
-
 path=$(nix-store -q $(nix-instantiate fixed.nix -A good.0))
 
 echo 'testing bad...'
diff --git a/tests/gc-auto.sh b/tests/gc-auto.sh
index de1e2cfe4..880742839 100644
--- a/tests/gc-auto.sh
+++ b/tests/gc-auto.sh
@@ -1,5 +1,7 @@
 source common.sh
 
+needLocalStore "“min-free” and “max-free” are daemon options"
+
 clearStore
 
 garbage1=$(nix add-to-store --name garbage1 ./nar-access.sh)
diff --git a/tests/init.sh b/tests/init.sh
index 19a12c1e2..cbbf8af9d 100644
--- a/tests/init.sh
+++ b/tests/init.sh
@@ -18,6 +18,7 @@ build-users-group =
 keep-derivations = false
 sandbox = false
 include nix.conf.extra
+trusted-users = $(whoami)
 EOF
 
 cat > "$NIX_CONF_DIR"/nix.conf.extra <<EOF
diff --git a/tests/linux-sandbox.sh b/tests/linux-sandbox.sh
index 52967d07d..dedf85daa 100644
--- a/tests/linux-sandbox.sh
+++ b/tests/linux-sandbox.sh
@@ -1,5 +1,7 @@
 source common.sh
 
+needLocalStore "the sandbox only runs on the builder side, so it makes no sense to test it with the daemon"
+
 clearStore
 
 if ! canUseSandbox; then exit; fi
diff --git a/tests/multiple-outputs.sh b/tests/multiple-outputs.sh
index bedbc39a4..db1695dc5 100644
--- a/tests/multiple-outputs.sh
+++ b/tests/multiple-outputs.sh
@@ -52,7 +52,7 @@ outPath2=$(nix-build $(nix-instantiate multiple-outputs.nix -A a.second) --no-ou
 
 # Delete one of the outputs and rebuild it.  This will cause a hash
 # rewrite.
-nix-store --delete $TEST_ROOT/result-second --ignore-liveness
+env -u NIX_REMOTE nix-store --delete $TEST_ROOT/result-second --ignore-liveness
 nix-build multiple-outputs.nix -A a.all -o $TEST_ROOT/result
 [ "$(cat $TEST_ROOT/result-second/file)" = "second" ]
 [ "$(cat $TEST_ROOT/result-second/link/file)" = "first" ]
diff --git a/tests/optimise-store.sh b/tests/optimise-store.sh
index 61e3df2f9..8c2d05cd5 100644
--- a/tests/optimise-store.sh
+++ b/tests/optimise-store.sh
@@ -26,7 +26,8 @@ if [ "$inode1" = "$inode3" ]; then
     exit 1
 fi
 
-nix-store --optimise
+# XXX: This should work through the daemon too
+NIX_REMOTE="" nix-store --optimise
 
 inode1="$(stat --format=%i $outPath1/foo)"
 inode3="$(stat --format=%i $outPath3/foo)"
diff --git a/tests/post-hook.sh b/tests/post-hook.sh
index a02657215..05eecc719 100644
--- a/tests/post-hook.sh
+++ b/tests/post-hook.sh
@@ -2,7 +2,12 @@ source common.sh
 
 clearStore
 
+rm -f $TEST_ROOT/result
+
 export REMOTE_STORE=$TEST_ROOT/remote_store
+echo 'require-sigs = false' >> $NIX_CONF_DIR/nix.conf
+
+restartDaemon
 
 # Build the dependencies and push them to the remote store
 nix-build -o $TEST_ROOT/result dependencies.nix --post-build-hook $PWD/push-to-store.sh
diff --git a/tests/referrers.sh b/tests/referrers.sh
index 8ab8e5ddf..d71bb5c4b 100644
--- a/tests/referrers.sh
+++ b/tests/referrers.sh
@@ -1,5 +1,7 @@
 source common.sh
 
+needLocalStore "uses some low-level store manipulations that aren’t available through the daemon"
+
 clearStore
 
 max=500
diff --git a/tests/repair.sh b/tests/repair.sh
index ec7ad5dca..6184e0bd5 100644
--- a/tests/repair.sh
+++ b/tests/repair.sh
@@ -1,5 +1,7 @@
 source common.sh
 
+needLocalStore "--repair needs a local store"
+
 clearStore
 
 path=$(nix-build dependencies.nix -o $TEST_ROOT/result)
diff --git a/tests/structured-attrs.sh b/tests/structured-attrs.sh
index 9ba2672b6..fcc00c4e0 100644
--- a/tests/structured-attrs.sh
+++ b/tests/structured-attrs.sh
@@ -1,5 +1,9 @@
 source common.sh
 
+# 27ce722638 required some incompatible changes to the nix file, so skip this
+# tests for the older versions
+requireDaemonNewerThan "2.4pre20210622"
+
 clearStore
 
 outPath=$(nix-build structured-attrs.nix --no-out-link)
diff --git a/tests/timeout.sh b/tests/timeout.sh
index eea9b5731..e3fb3ebcc 100644
--- a/tests/timeout.sh
+++ b/tests/timeout.sh
@@ -2,6 +2,8 @@
 
 source common.sh
 
+# XXX: This shouldn’t be, but #4813 cause this test to fail
+needLocalStore "see #4813"
 
 set +e
 messages=$(nix-build -Q timeout.nix -A infiniteLoop --timeout 2 2>&1)