diff --git a/tests/binary-cache.sh b/tests/binary-cache.sh
index 6697ce236..d7bc1507b 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"
+
 # We can produce drvs directly into the binary cache
 clearStore
 clearCacheCache
diff --git a/tests/ca/build-with-garbage-path.sh b/tests/ca/build-with-garbage-path.sh
index e6f878702..9aa08a899 100755
--- a/tests/ca/build-with-garbage-path.sh
+++ b/tests/ca/build-with-garbage-path.sh
@@ -3,7 +3,8 @@
 # Regression test for https://github.com/NixOS/nix/issues/4858
 
 source common.sh
-sed -i 's/experimental-features .*/& ca-derivations ca-references/' "$NIX_CONF_DIR"/nix.conf
+
+requireDaemonNewerThan "2.4pre20210621"
 
 # Get the output path of `rootCA`, and put some garbage instead
 outPath="$(nix-build ./content-addressed.nix -A rootCA --no-out-link)"
diff --git a/tests/ca/common.sh b/tests/ca/common.sh
index e083d873c..c5aa34334 100644
--- a/tests/ca/common.sh
+++ b/tests/ca/common.sh
@@ -1 +1,5 @@
 source ../common.sh
+
+sed -i 's/experimental-features .*/& ca-derivations ca-references/' "$NIX_CONF_DIR"/nix.conf
+
+restartDaemon
diff --git a/tests/ca/concurrent-builds.sh b/tests/ca/concurrent-builds.sh
index 68441ec76..b442619e2 100755
--- a/tests/ca/concurrent-builds.sh
+++ b/tests/ca/concurrent-builds.sh
@@ -5,7 +5,7 @@
 
 source common.sh
 
-sed -i 's/experimental-features .*/& ca-derivations ca-references/' "$NIX_CONF_DIR"/nix.conf
+buggyNeedLocalStore "For some reason, this deadlocks with the daemon"
 
 export NIX_TESTS_CA_BY_DEFAULT=1
 
diff --git a/tests/ca/duplicate-realisation-in-closure.sh b/tests/ca/duplicate-realisation-in-closure.sh
index ca9099641..74c5d25fd 100644
--- a/tests/ca/duplicate-realisation-in-closure.sh
+++ b/tests/ca/duplicate-realisation-in-closure.sh
@@ -1,5 +1,7 @@
 source ./common.sh
 
+requireDaemonNewerThan "2.4pre20210625"
+
 sed -i 's/experimental-features .*/& ca-derivations ca-references/' "$NIX_CONF_DIR"/nix.conf
 
 export REMOTE_STORE_DIR="$TEST_ROOT/remote_store"
diff --git a/tests/ca/gc.sh b/tests/ca/gc.sh
index e4f9857d6..e9b6c5ab5 100755
--- a/tests/ca/gc.sh
+++ b/tests/ca/gc.sh
@@ -4,8 +4,6 @@
 
 source common.sh
 
-sed -i 's/experimental-features .*/& ca-derivations ca-references/' "$NIX_CONF_DIR"/nix.conf
-
 export NIX_TESTS_CA_BY_DEFAULT=1
 
 cd ..
diff --git a/tests/ca/post-hook.sh b/tests/ca/post-hook.sh
index 4b8da4cd8..1c9d4f700 100755
--- a/tests/ca/post-hook.sh
+++ b/tests/ca/post-hook.sh
@@ -2,6 +2,8 @@
 
 source common.sh
 
+requireDaemonNewerThan "2.4pre20210626"
+
 sed -i 's/experimental-features .*/& ca-derivations ca-references nix-command flakes/' "$NIX_CONF_DIR"/nix.conf
 
 export NIX_TESTS_CA_BY_DEFAULT=1
diff --git a/tests/ca/recursive.sh b/tests/ca/recursive.sh
index d9281d91f..648bf0a91 100755
--- a/tests/ca/recursive.sh
+++ b/tests/ca/recursive.sh
@@ -2,6 +2,8 @@
 
 source common.sh
 
+requireDaemonNewerThan "2.4pre20210623"
+
 sed -i 's/experimental-features .*/& ca-derivations ca-references nix-command flakes/' "$NIX_CONF_DIR"/nix.conf
 
 export NIX_TESTS_CA_BY_DEFAULT=1
diff --git a/tests/ca/substitute.sh b/tests/ca/substitute.sh
index c80feaacf..3d9001bb8 100644
--- a/tests/ca/substitute.sh
+++ b/tests/ca/substitute.sh
@@ -4,7 +4,7 @@
 
 source common.sh
 
-sed -i 's/experimental-features .*/& ca-derivations ca-references/' "$NIX_CONF_DIR"/nix.conf
+needLocalStore "“--no-require-sigs” can’t be used with the daemon"
 
 rm -rf $TEST_ROOT/binary_cache
 
diff --git a/tests/check.sh b/tests/check.sh
index d26d4d8fc..ab48ff865 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"
+
 checkBuildTempDirRemoved ()
 {
     buildDir=$(sed -n 's/CHECK_TMPDIR=//p' $1 | head -1)
diff --git a/tests/common.sh.in b/tests/common.sh.in
index d31d3fbb8..bc2e0931f 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
@@ -45,6 +49,9 @@ export busybox="@sandbox_shell@"
 export version=@PACKAGE_VERSION@
 export system=@system@
 
+export IMPURE_VAR1=foo
+export IMPURE_VAR2=bar
+
 cacheDir=$TEST_ROOT/binary-cache
 
 readLink() {
@@ -75,6 +82,10 @@ 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 $NIX_STATE_DIR/daemon-socket/socket
@@ -84,20 +95,44 @@ startDaemon() {
         sleep 1
     done
     pidDaemon=$!
-    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..."
@@ -123,4 +158,22 @@ 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/db-migration.sh b/tests/db-migration.sh
index e0ff7d311..3f9dc8972 100644
--- a/tests/db-migration.sh
+++ b/tests/db-migration.sh
@@ -3,11 +3,14 @@
 # Only run this if we have an older Nix available
 # XXX: This assumes that the `daemon` package is older than the `client` one
 if [[ -z "$NIX_DAEMON_PACKAGE" ]]; then
-    exit 0
+    exit 99
 fi
 
 source common.sh
 
+killDaemon
+unset NIX_REMOTE
+
 # Fill the db using the older Nix
 PATH_WITH_NEW_NIX="$PATH"
 export PATH="$NIX_DAEMON_PACKAGE/bin:$PATH"
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/eval-store.sh b/tests/eval-store.sh
index 7bb86d77c..9ab7a87be 100644
--- a/tests/eval-store.sh
+++ b/tests/eval-store.sh
@@ -1,5 +1,7 @@
 source common.sh
 
+requireDaemonNewerThan "2.4pre20210727"
+
 eval_store=$TEST_ROOT/eval-store
 
 clearStore
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 6867f2eb4..521d9e539 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 store add-path --name garbage1 ./nar-access.sh)
diff --git a/tests/init.sh b/tests/init.sh
index 6e45a939f..3c6d5917d 100644
--- a/tests/init.sh
+++ b/tests/init.sh
@@ -23,6 +23,7 @@ substituters =
 flake-registry = $TEST_ROOT/registry.json
 show-trace = true
 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 eac62d461..3f304ac2f 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 99; fi
diff --git a/tests/multiple-outputs.sh b/tests/multiple-outputs.sh
index de573d4fa..0bca12b42 100644
--- a/tests/multiple-outputs.sh
+++ b/tests/multiple-outputs.sh
@@ -58,7 +58,7 @@ 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 238a8f826..049e40749 100644
--- a/tests/post-hook.sh
+++ b/tests/post-hook.sh
@@ -5,6 +5,9 @@ clearStore
 rm -f $TEST_ROOT/result
 
 export REMOTE_STORE=file:$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 614dd8f5b..81323c280 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 ba019028d..12dcde8ea 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 9612020b8..e585ce37f 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
 
 rm -f $TEST_ROOT/result
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)