diff --git a/test/integration-tests/TEST-55-OOMD/TEST-55-OOMD.units/TEST-55-OOMD-testbloat.service b/test/integration-tests/TEST-55-OOMD/TEST-55-OOMD.units/TEST-55-OOMD-testbloat.service
index 22bbd210e96..e4109fd60dd 100644
--- a/test/integration-tests/TEST-55-OOMD/TEST-55-OOMD.units/TEST-55-OOMD-testbloat.service
+++ b/test/integration-tests/TEST-55-OOMD/TEST-55-OOMD.units/TEST-55-OOMD-testbloat.service
@@ -7,7 +7,6 @@ Description=Create a lot of memory pressure
 # to throttle and be put under heavy pressure.
 MemoryHigh=3M
 Slice=TEST-55-OOMD-workload.slice
-# Pin --vm-method to a portable method (zero-one): the default 'all' cycles
-# through methods, including newer ones using AVX-512 instructions that SIGILL
-# on CPUs without AVX-512 (e.g. AMD Zen 1-3), making the test flaky.
-ExecStart=stress-ng --timeout 3m --vm 10 --vm-bytes 200M --vm-keep --vm-method=zero-one
+# Pin --vm-method=lfsr32: the only stress-ng vm method without TARGET_CLONES,
+# so it can't dispatch to an AVX-512 clone and SIGILL on CPUs lacking it.
+ExecStart=stress-ng --timeout 3m --vm 10 --vm-bytes 200M --vm-keep --vm-method=lfsr32
diff --git a/test/integration-tests/TEST-55-OOMD/TEST-55-OOMD.units/TEST-55-OOMD-testmunch.service b/test/integration-tests/TEST-55-OOMD/TEST-55-OOMD.units/TEST-55-OOMD-testmunch.service
index 06eea10b79a..81305c7e974 100644
--- a/test/integration-tests/TEST-55-OOMD/TEST-55-OOMD.units/TEST-55-OOMD-testmunch.service
+++ b/test/integration-tests/TEST-55-OOMD/TEST-55-OOMD.units/TEST-55-OOMD-testmunch.service
@@ -5,7 +5,6 @@ Description=Create some memory pressure
 [Service]
 MemoryHigh=12M
 Slice=TEST-55-OOMD-workload.slice
-# Pin --vm-method to a portable method (zero-one): the default 'all' cycles
-# through methods, including newer ones using AVX-512 instructions that SIGILL
-# on CPUs without AVX-512 (e.g. AMD Zen 1-3), making the test flaky.
-ExecStart=stress-ng --timeout 3m --vm 10 --vm-bytes 200M --vm-keep --vm-method=zero-one
+# Pin --vm-method=lfsr32: the only stress-ng vm method without TARGET_CLONES,
+# so it can't dispatch to an AVX-512 clone and SIGILL on CPUs lacking it.
+ExecStart=stress-ng --timeout 3m --vm 10 --vm-bytes 200M --vm-keep --vm-method=lfsr32
diff --git a/test/units/TEST-07-PID1.socket-on-failure.sh b/test/units/TEST-07-PID1.socket-on-failure.sh
index 44b8a43634f..ff947b10e26 100755
--- a/test/units/TEST-07-PID1.socket-on-failure.sh
+++ b/test/units/TEST-07-PID1.socket-on-failure.sh
@@ -65,9 +65,8 @@ mkdir "/tmp/$UNIT_NAME/test"
 systemctl is-failed "$UNIT_NAME.socket"
 assert_eq "$(systemctl show "$UNIT_NAME.socket" -P SubState)" "failed"
 
-timeout --foreground 60 bash -c "while [[ -d '/tmp/$UNIT_NAME/test' ]]; do sleep .5; done"
+timeout --foreground 60 bash -c "until systemctl is-active TEST-07-PID1-socket-OnFailure.service; do sleep .5; done"
 [[ ! -e "/tmp/$UNIT_NAME/test" ]]
-systemctl is-active TEST-07-PID1-socket-OnFailure.service
 
 systemctl start "$UNIT_NAME.socket"
 systemctl is-active "$UNIT_NAME.socket"
diff --git a/test/units/TEST-55-OOMD.sh b/test/units/TEST-55-OOMD.sh
index b7311e83dca..84baee12a42 100755
--- a/test/units/TEST-55-OOMD.sh
+++ b/test/units/TEST-55-OOMD.sh
@@ -366,13 +366,12 @@ EOF
     systemctl reload systemd-oomd.service
 
     # Run a transient service with OOMRules=testrule that generates memory pressure.
-    # Pin --vm-method to a portable method (zero-one): the default 'all' cycles
-    # through every method, including newer ones using AVX-512 instructions that
-    # SIGILL on CPUs without AVX-512 (e.g. AMD Zen 1-3), making the test flaky.
+    # Pin --vm-method=lfsr32: the only stress-ng vm method without TARGET_CLONES,
+    # so it can't dispatch to an AVX-512 clone and SIGILL on CPUs lacking it.
     (! systemd-run --wait --unit=TEST-55-OOMD-testrules \
         -p MemoryHigh=3M \
         -p OOMRules=testrule \
-        stress-ng --timeout 3m --vm 10 --vm-bytes 50M --vm-keep --vm-method=zero-one)
+        stress-ng --timeout 3m --vm 10 --vm-bytes 50M --vm-keep --vm-method=lfsr32)
 
     # Verify in the journal that the rule triggered
     journalctl --sync
@@ -457,14 +456,12 @@ EOF
 
     # Start the unit without --wait so we can check mid-run state. The
     # stress-ng timeout bounds the test if anything goes wrong.
-    # Pin --vm-method to a portable method (zero-one): the default 'all' cycles
-    # through every method, including newer ones using AVX-512 instructions that
-    # SIGILL on CPUs without AVX-512 (e.g. AMD Zen 1-3) and would cause stress-ng
-    # to exit before the 6 s wait below elapses, failing the ActiveState check.
+    # Pin --vm-method=lfsr32: the only stress-ng vm method without TARGET_CLONES,
+    # so it can't SIGILL on AVX-512-less CPUs and exit before the 6 s wait below.
     systemd-run --unit=TEST-55-OOMD-slowrule \
         -p MemoryHigh=3M \
         -p OOMRules=slowrule \
-        stress-ng --timeout 15s --vm 10 --vm-bytes 50M --vm-keep --vm-method=zero-one
+        stress-ng --timeout 15s --vm 10 --vm-bytes 50M --vm-keep --vm-method=lfsr32
 
     # Wait long enough for oomd's 1s rule-check loop to evaluate the condition
     # many times. With LastingSec=1h the kill must not fire.