diff --git a/.gitlab/pipeline/zombienet/bridges.yml b/.gitlab/pipeline/zombienet/bridges.yml
index f2de526c8705..16cabad6ccab 100644
--- a/.gitlab/pipeline/zombienet/bridges.yml
+++ b/.gitlab/pipeline/zombienet/bridges.yml
@@ -53,3 +53,10 @@ zombienet-bridges-0001-asset-transfer-works:
   script:
     - /home/nonroot/bridges-polkadot-sdk/bridges/zombienet/run-new-test.sh 0001-asset-transfer --docker
     - echo "Done"
+
+zombienet-bridges-0002-mandatory-headers-synced-while-idle:
+  extends:
+    - .zombienet-bridges-common
+  script:
+    - /home/nonroot/bridges-polkadot-sdk/bridges/zombienet/run-new-test.sh 0002-mandatory-headers-synced-while-idle --docker
+    - echo "Done"
diff --git a/bridges/zombienet/environments/rococo-westend/spawn.sh b/bridges/zombienet/environments/rococo-westend/spawn.sh
index dbdc58d5fa1b..550eee04bd6e 100755
--- a/bridges/zombienet/environments/rococo-westend/spawn.sh
+++ b/bridges/zombienet/environments/rococo-westend/spawn.sh
@@ -4,11 +4,11 @@ set -e
 
 trap "trap - SIGTERM && kill -9 -$$" SIGINT SIGTERM EXIT
 
-source "${BASH_SOURCE%/*}/../../utils/common.sh"
 source "${BASH_SOURCE%/*}/../../utils/zombienet.sh"
 
 # whether to init the chains (open HRMP channels, set XCM version, create reserve assets, etc)
 init=0
+start_relayer=0
 while [ $# -ne 0 ]
 do
     arg="$1"
@@ -16,6 +16,9 @@ do
         --init)
             init=1
             ;;
+        --start-relayer)
+            start_relayer=1
+            ;;
     esac
     shift
 done
@@ -55,17 +58,13 @@ if [[ $init -eq 1 ]]; then
   run_zndsl ${BASH_SOURCE%/*}/westend-init.zndsl $westend_dir
 fi
 
-relay_log=$logs_dir/relay.log
-echo -e "Starting rococo-westend relay. Logs available at: $relay_log\n"
-start_background_process "$helper_script run-relay" $relay_log relay_pid
+if [[ $start_relayer -eq 1 ]]; then
+  ${BASH_SOURCE%/*}/start_relayer.sh $rococo_dir $westend_dir relayer_pid
+fi
 
-run_zndsl ${BASH_SOURCE%/*}/rococo.zndsl $rococo_dir
 echo $rococo_dir > $TEST_DIR/rococo.env
-echo
-
-run_zndsl ${BASH_SOURCE%/*}/westend.zndsl $westend_dir
 echo $westend_dir > $TEST_DIR/westend.env
 echo
 
-wait -n $rococo_pid $westend_pid $relay_pid
+wait -n $rococo_pid $westend_pid $relayer_pid
 kill -9 -$$
diff --git a/bridges/zombienet/environments/rococo-westend/start_relayer.sh b/bridges/zombienet/environments/rococo-westend/start_relayer.sh
new file mode 100755
index 000000000000..c57d4f1a4374
--- /dev/null
+++ b/bridges/zombienet/environments/rococo-westend/start_relayer.sh
@@ -0,0 +1,23 @@
+#!/bin/bash
+
+set -e
+
+source "${BASH_SOURCE%/*}/../../utils/common.sh"
+source "${BASH_SOURCE%/*}/../../utils/zombienet.sh"
+
+rococo_dir=$1
+westend_dir=$2
+__relayer_pid=$3
+
+logs_dir=$TEST_DIR/logs
+helper_script="${BASH_SOURCE%/*}/helper.sh"
+
+relayer_log=$logs_dir/relayer.log
+echo -e "Starting rococo-westend relayer. Logs available at: $relayer_log\n"
+start_background_process "$helper_script run-relay" $relayer_log relayer_pid
+
+run_zndsl ${BASH_SOURCE%/*}/rococo.zndsl $rococo_dir
+run_zndsl ${BASH_SOURCE%/*}/westend.zndsl $westend_dir
+
+eval $__relayer_pid="'$relayer_pid'"
+
diff --git a/bridges/zombienet/helpers/only-mandatory-headers-synced-when-idle.js b/bridges/zombienet/helpers/only-mandatory-headers-synced-when-idle.js
index 3a3432cfaf38..979179245ebe 100644
--- a/bridges/zombienet/helpers/only-mandatory-headers-synced-when-idle.js
+++ b/bridges/zombienet/helpers/only-mandatory-headers-synced-when-idle.js
@@ -10,7 +10,7 @@ async function run(nodeName, networkInfo, args) {
 
     // start listening to new blocks
     let totalGrandpaHeaders = 0;
-    let totalParachainHeaders = 0;
+    let initialParachainHeaderImported = false;
     api.rpc.chain.subscribeNewHeads(async function (header) {
         const apiAtParent = await api.at(header.parentHash);
         const apiAtCurrent = await api.at(header.hash);
@@ -22,7 +22,7 @@ async function run(nodeName, networkInfo, args) {
             apiAtCurrent,
             currentEvents,
         );
-        totalParachainHeaders += await utils.ensureOnlyInitialParachainHeaderImported(
+        initialParachainHeaderImported = await utils.ensureOnlyInitialParachainHeaderImported(
             bridgedChain,
             apiAtParent,
             apiAtCurrent,
@@ -36,7 +36,7 @@ async function run(nodeName, networkInfo, args) {
     if (totalGrandpaHeaders == 0) {
         throw new Error("No bridged relay chain headers imported");
     }
-    if (totalParachainHeaders == 0) {
+    if (!initialParachainHeaderImported) {
         throw new Error("No bridged parachain headers imported");
     }
 }
diff --git a/bridges/zombienet/helpers/utils.js b/bridges/zombienet/helpers/utils.js
index 5a5542b56dfc..f6e9f5623b47 100644
--- a/bridges/zombienet/helpers/utils.js
+++ b/bridges/zombienet/helpers/utils.js
@@ -98,6 +98,6 @@ module.exports = {
             throw new Error("Unexpected parachain header import: " + newParachainHeaders + " / " + maxNewParachainHeaders);
         }
 
-        return newParachainHeaders;
+        return hasBestBridgedParachainHeader;
     },
 }
diff --git a/bridges/zombienet/run-new-test.sh b/bridges/zombienet/run-new-test.sh
index 3bfcb6d83e9a..2ed2a412b8a7 100755
--- a/bridges/zombienet/run-new-test.sh
+++ b/bridges/zombienet/run-new-test.sh
@@ -2,6 +2,8 @@
 
 set -e
 
+trap 'kill -9 -$$ || echo "Environment already teared down"' SIGINT SIGTERM EXIT
+
 test=$1
 shift
 
@@ -43,5 +45,3 @@ export TEST_DIR=`mktemp -d /tmp/bridges-tests-run-XXXXX`
 echo -e "Test folder: $TEST_DIR\n"
 
 ${BASH_SOURCE%/*}/tests/$test/run.sh
-
-kill -9 -$$ || echo "Environment already teared down"
\ No newline at end of file
diff --git a/bridges/zombienet/tests/0001-asset-transfer/run.sh b/bridges/zombienet/tests/0001-asset-transfer/run.sh
index 07951a0e321a..8a053ee72097 100755
--- a/bridges/zombienet/tests/0001-asset-transfer/run.sh
+++ b/bridges/zombienet/tests/0001-asset-transfer/run.sh
@@ -5,7 +5,7 @@ set -e
 source "${BASH_SOURCE%/*}/../../utils/common.sh"
 source "${BASH_SOURCE%/*}/../../utils/zombienet.sh"
 
-${BASH_SOURCE%/*}/../../environments/rococo-westend/spawn.sh --init &
+${BASH_SOURCE%/*}/../../environments/rococo-westend/spawn.sh --init --start-relayer &
 env_pid=$!
 
 ensure_process_file $env_pid $TEST_DIR/rococo.env 400
diff --git a/bridges/zombienet/tests/0002-mandatory-headers-synced-while-idle/rococo-to-westend.zndsl b/bridges/zombienet/tests/0002-mandatory-headers-synced-while-idle/rococo-to-westend.zndsl
new file mode 100644
index 000000000000..d4283b361296
--- /dev/null
+++ b/bridges/zombienet/tests/0002-mandatory-headers-synced-while-idle/rococo-to-westend.zndsl
@@ -0,0 +1,8 @@
+Description: While relayer is idle, we only sync mandatory Rococo (and a single Rococo BH) headers to Westend BH.
+Network: ../../../../cumulus/zombienet/bridge-hubs/bridge_hub_westend_local_network.toml
+Creds: config
+
+# ensure that relayer is only syncing mandatory headers while idle. This includes both headers that were
+# generated while relay was offline and those in the next 100 seconds while script is active.
+bridge-hub-westend-collator1: js-script ../../helpers/only-mandatory-headers-synced-when-idle.js with "300,rococo-at-westend" within 600 seconds
+
diff --git a/bridges/zombienet/tests/0002-mandatory-headers-synced-while-idle/run.sh b/bridges/zombienet/tests/0002-mandatory-headers-synced-while-idle/run.sh
new file mode 100755
index 000000000000..423f4a1bcc0f
--- /dev/null
+++ b/bridges/zombienet/tests/0002-mandatory-headers-synced-while-idle/run.sh
@@ -0,0 +1,35 @@
+#!/bin/bash
+
+set -e
+
+source "${BASH_SOURCE%/*}/../../utils/common.sh"
+source "${BASH_SOURCE%/*}/../../utils/zombienet.sh"
+
+# We use `--relayer-delay` in order to sleep some time before starting relayer.
+# We want to sleep for at least 1 session, which is expected to be 60 seconds for test environment.
+${BASH_SOURCE%/*}/../../environments/rococo-westend/spawn.sh &
+env_pid=$!
+
+ensure_process_file $env_pid $TEST_DIR/rococo.env 400
+rococo_dir=`cat $TEST_DIR/rococo.env`
+echo
+
+ensure_process_file $env_pid $TEST_DIR/westend.env 180
+westend_dir=`cat $TEST_DIR/westend.env`
+echo
+
+# Sleep for some time before starting the relayer. We want to sleep for at least 1 session,
+# which is expected to be 60 seconds for the test environment.
+echo -e "Sleeping 90s before starting relayer ...\n"
+sleep 90
+${BASH_SOURCE%/*}/../../environments/rococo-westend/start_relayer.sh $rococo_dir $westend_dir relayer_pid
+
+# Sometimes the relayer syncs multiple parachain heads in the begining leading to test failures.
+# See issue: https://github.com/paritytech/parity-bridges-common/issues/2838.
+# TODO: Remove this sleep after the issue is fixed.
+echo -e "Sleeping 180s before runing the tests ...\n"
+sleep 180
+
+run_zndsl ${BASH_SOURCE%/*}/rococo-to-westend.zndsl $westend_dir
+run_zndsl ${BASH_SOURCE%/*}/westend-to-rococo.zndsl $rococo_dir
+
diff --git a/bridges/zombienet/tests/0002-mandatory-headers-synced-while-idle/westend-to-rococo.zndsl b/bridges/zombienet/tests/0002-mandatory-headers-synced-while-idle/westend-to-rococo.zndsl
new file mode 100644
index 000000000000..1ea4c92a3458
--- /dev/null
+++ b/bridges/zombienet/tests/0002-mandatory-headers-synced-while-idle/westend-to-rococo.zndsl
@@ -0,0 +1,7 @@
+Description: While relayer is idle, we only sync mandatory Westend (and a single Westend BH) headers to Rococo BH.
+Network: ../../../../cumulus/zombienet/bridge-hubs/bridge_hub_rococo_local_network.toml
+Creds: config
+
+# ensure that relayer is only syncing mandatory headers while idle. This includes both headers that were
+# generated while relay was offline and those in the next 100 seconds while script is active.
+bridge-hub-rococo-collator1: js-script ../../helpers/only-mandatory-headers-synced-when-idle.js with "300,westend-at-rococo" within 600 seconds