diff --git a/test/system/030-run.bats b/test/system/030-run.bats
index 6da1a817a8..bb12bf6826 100644
--- a/test/system/030-run.bats
+++ b/test/system/030-run.bats
@@ -778,7 +778,7 @@ json-file | f
 @test "podman run --timeout - basic test" {
     cid=timeouttest
     t0=$SECONDS
-    run_podman 255 run --name $cid --timeout 10 $IMAGE sleep 60
+    run_podman 255 run --name $cid --timeout 2 $IMAGE sleep 60
     t1=$SECONDS
     # Confirm that container is stopped. Podman-remote unfortunately
     # cannot tell the difference between "stopped" and "exited", and
@@ -790,8 +790,8 @@ json-file | f
     # This operation should take
     # exactly 10 seconds. Give it some leeway.
     delta_t=$(( $t1 - $t0 ))
-    assert "$delta_t" -gt  8 "podman stop: ran too quickly!"
-    assert "$delta_t" -le 14 "podman stop: took too long"
+    assert "$delta_t" -gt 1 "podman stop: ran too quickly!"
+    assert "$delta_t" -le 6 "podman stop: took too long"
 
     run_podman rm $cid
 }
diff --git a/test/system/075-exec.bats b/test/system/075-exec.bats
index 53f0c20b55..0c0f7cab8f 100644
--- a/test/system/075-exec.bats
+++ b/test/system/075-exec.bats
@@ -136,20 +136,6 @@ load helpers
     run_podman rm -t 0 -f $cid
 }
 
-@test "podman exec --wait" {
-    skip_if_remote "test is meaningless over remote"
-
-    # wait on bogus container
-    run_podman 125 exec --wait 5 "bogus_container" echo hello
-    assert "$output" = "Error: timed out waiting for container: bogus_container"
-
-    run_podman create --name "wait_container" $IMAGE top
-    run_podman 255 exec --wait 5 "wait_container" echo hello
-    assert "$output" = "Error: can only create exec sessions on running containers: container state improper"
-
-    run_podman rm -f wait_container
-}
-
 @test "podman run umask" {
     umask="0724"
     run_podman run --rm -q $IMAGE grep Umask /proc/self/status
diff --git a/test/system/090-events.bats b/test/system/090-events.bats
index 072d7f9f4f..993d7beebc 100644
--- a/test/system/090-events.bats
+++ b/test/system/090-events.bats
@@ -7,41 +7,34 @@ load helpers
 load helpers.network
 
 # bats test_tags=distro-integration
-@test "events with a filter by label" {
+@test "events with a filter by label and --no-trunc option" {
     cname=test-$(random_string 30 | tr A-Z a-z)
     labelname=$(random_string 10)
     labelvalue=$(random_string 15)
 
-    run_podman run --label $labelname=$labelvalue --name $cname --rm $IMAGE ls
+    before=$(date --iso-8601=seconds)
+    run_podman run -d --label $labelname=$labelvalue --name $cname --rm $IMAGE true
+    id="$output"
 
-    expect=".* container start [0-9a-f]\+ (image=$IMAGE, name=$cname,.* ${labelname}=${labelvalue}"
-    run_podman events --filter type=container -f container=$cname --filter label=${labelname}=${labelvalue} --filter event=start --stream=false
+    expect=".* container start $id (image=$IMAGE, name=$cname,.* ${labelname}=${labelvalue}"
+    run_podman events --since "$before"  --filter type=container -f container=$cname --filter label=${labelname}=${labelvalue} --filter event=start --stream=false
     is "$output" "$expect" "filtering by container name and label"
 
     # Same thing, but without the container-name filter
-    run_podman system events -f type=container --filter label=${labelname}=${labelvalue} --filter event=start --stream=false
+    run_podman system events --since "$before" -f type=container --filter label=${labelname}=${labelvalue} --filter event=start --stream=false
     is "$output" "$expect" "filtering just by label"
 
     # Now filter just by container name, no label
-    run_podman events --filter type=container --filter container=$cname --filter event=start --stream=false
+    run_podman events --since "$before" --filter type=container --filter container=$cname --filter event=start --stream=false
     is "$output" "$expect" "filtering just by container"
-}
-
-@test "truncate events" {
-    cname=test-$(random_string 30 | tr A-Z a-z)
-
-    run_podman run -d --name=$cname --rm $IMAGE echo hi
-    id="$output"
-
-    run_podman events --filter container=$cname --filter event=start --stream=false
-    is "$output" ".* $id " "filtering by container name full id"
 
+    # check --no-trunc=false
     truncID=${id:0:12}
-    run_podman events --filter container=$cname --filter event=start --stream=false --no-trunc=false
+    run_podman events --since "$before" --filter container=$cname --filter event=start --stream=false --no-trunc=false
     is "$output" ".* $truncID " "filtering by container name trunc id"
 
     # --no-trunc does not affect --format; we always get the full ID
-    run_podman events --filter container=$cname --filter event=died --stream=false --format='{{.ID}}--{{.Image}}' --no-trunc=false
+    run_podman events --since "$before" --filter container=$cname --filter event=died --stream=false --format='{{.ID}}--{{.Image}}' --no-trunc=false
     assert "$output" = "${id}--${IMAGE}"
 }
 
diff --git a/test/system/250-systemd.bats b/test/system/250-systemd.bats
index bf4d4a5180..832ee0d742 100644
--- a/test/system/250-systemd.bats
+++ b/test/system/250-systemd.bats
@@ -142,14 +142,16 @@ function service_cleanup() {
 @test "podman generate systemd - envar" {
     cname=$(random_string)
     FOO=value BAR=%s run_podman create --name $cname --env FOO -e BAR --env MYVAR=myval \
-        $IMAGE sh -c 'printenv && sleep 100'
+        $IMAGE sh -c 'printenv && echo READY; trap 'exit' SIGTERM; while :; do sleep 0.1; done'
 
     # Start systemd service to run this container
     service_setup
 
-    # Give container time to start; make sure output looks top-like
-    sleep 2
-    run_podman logs $cname
+    # Give container time to start and print output
+    # wait_for_ready returns directly if the logs matches and preserves $output
+    # for us so we do not have to call podman logs again here if we match the env below.
+    wait_for_ready $cname
+
     is "$output" ".*FOO=value.*" "FOO environment variable set"
     is "$output" ".*BAR=%s.*" "BAR environment variable set"
     is "$output" ".*MYVAR=myval.*" "MYVAL environment variable set"
@@ -397,13 +399,13 @@ spec:
   - command:
     - sh
     - -c
-    - echo a stdout; echo a stderr 1>&2; sleep inf
+    - echo a stdout; echo a stderr 1>&2; trap 'exit' SIGTERM; while :; do sleep 0.1; done
     image: $IMAGE
     name: a
   - command:
     - sh
     - -c
-    - echo b stdout; echo b stderr 1>&2; sleep inf
+    - echo b stdout; echo b stderr 1>&2; trap 'exit' SIGTERM; while :; do sleep 0.1; done
     image: $IMAGE
     name: b
 EOF
diff --git a/test/system/255-auto-update.bats b/test/system/255-auto-update.bats
index f870546aca..eac97801ed 100644
--- a/test/system/255-auto-update.bats
+++ b/test/system/255-auto-update.bats
@@ -132,7 +132,6 @@ function _confirm_update() {
     # Image has already been pulled, so this shouldn't take too long
     local timeout=10
     while [[ $timeout -gt 0 ]]; do
-        sleep 1
         run_podman '?' inspect --format "{{.Image}}" $cname
         if [[ $status != 0 ]]; then
             if [[ $output =~ (no such object|does not exist in database): ]]; then
@@ -144,6 +143,7 @@ function _confirm_update() {
         elif [[ $output != $old_iid ]]; then
             return
         fi
+        sleep 1
         timeout=$((timeout - 1))
     done
 
@@ -417,7 +417,7 @@ EOF
 Description=Podman auto-update testing timer
 
 [Timer]
-OnCalendar=*-*-* *:*:0/2
+OnActiveSec=0s
 Persistent=true
 
 [Install]
diff --git a/test/system/260-sdnotify.bats b/test/system/260-sdnotify.bats
index 315fdc2fed..a0aa6554ff 100644
--- a/test/system/260-sdnotify.bats
+++ b/test/system/260-sdnotify.bats
@@ -475,31 +475,41 @@ none | true  | false | 0
 none | false | false | 0
 "
 
-    # I am sorry, this is a long test as we need to test the upper matrix
-    # twice. The first run is using the default sdnotify policy of "ignore".
+    # In each iteration we switch between the sdnotify policy ignore and conmon.
+    # We could run them in a loop for each case but the test is slow so let's
+    # just switch between them as it should cover both policies sufficiently.
+    # Note because of this make sure to have at least two exit code cases directly
+    # after each other above so both polices will get at least once the error case.
+    # The first run is using the default sdnotify policy of "ignore".
     # In this case, the service container serves as the main PID of the service
     # to have a minimal resource footprint.  The second run is using the
     # "conmon" sdnotify policy in which case Podman needs to serve as the main
     # PID to act as an sdnotify proxy; there Podman will wait for the service
     # container to exit and reflects its exit code.
+    sdnotify_policy=ignore
     while read exit_code_prop cmd1 cmd2 exit_code; do
-        for sdnotify_policy in ignore conmon; do
-            generate_exit_code_yaml $fname $cmd1 $cmd2 $sdnotify_policy
-            yaml_sha=$(sha256sum $fname)
-            service_container="${yaml_sha:0:12}-service"
-            podman_exit=$exit_code
-            if [[ $sdnotify_policy == "ignore" ]];then
-                 podman_exit=0
-            fi
-            run_podman $podman_exit kube play --service-exit-code-propagation="$exit_code_prop" --service-container $fname
-            # Make sure that there are no error logs (e.g., #19715)
-            assert "$output" !~ "error msg="
-            run_podman container inspect --format '{{.KubeExitCodePropagation}}' $service_container
-            is "$output" "$exit_code_prop" "service container has the expected policy set in its annotations"
-            run_podman wait $service_container
-            is "$output" "$exit_code" "service container exit code (propagation: $exit_code_prop, policy: $service_policy, cmds: $cmd1 + $cmd2)"
-            run_podman kube down $fname
-        done
+        generate_exit_code_yaml $fname $cmd1 $cmd2 $sdnotify_policy
+        yaml_sha=$(sha256sum $fname)
+        service_container="${yaml_sha:0:12}-service"
+        podman_exit=$exit_code
+        if [[ $sdnotify_policy == "ignore" ]];then
+             podman_exit=0
+        fi
+        run_podman $podman_exit kube play --service-exit-code-propagation="$exit_code_prop" --service-container $fname
+        # Make sure that there are no error logs (e.g., #19715)
+        assert "$output" !~ "error msg="
+        run_podman container inspect --format '{{.KubeExitCodePropagation}}' $service_container
+        is "$output" "$exit_code_prop" "service container has the expected policy set in its annotations"
+        run_podman wait $service_container
+        is "$output" "$exit_code" "service container exit code (propagation: $exit_code_prop, policy: $sdnotify_policy, cmds: $cmd1 + $cmd2)"
+        run_podman kube down $fname
+
+        # in each iteration switch between conmon/ignore policy to get coverage for both
+        if [[ $sdnotify_policy == "ignore" ]]; then
+            sdnotify_policy=conmon
+        else
+            sdnotify_policy=ignore
+        fi
     done < <(parse_table "$exit_tests")
 
     # A final smoke test to make sure bogus policies lead to an error
diff --git a/test/system/700-play.bats b/test/system/700-play.bats
index 1441775748..c36ed04b9b 100644
--- a/test/system/700-play.bats
+++ b/test/system/700-play.bats
@@ -633,21 +633,33 @@ EOF
 # kube play --wait=true, where we clear up the created containers, pods, and volumes when a kill or sigterm is triggered
 @test "podman kube play --wait with siginterrupt" {
     cname=c$(random_string 15)
-    fname="/tmp/play_kube_wait_$(random_string 6).yaml"
-    run_podman container create --name $cname $IMAGE top
-    run_podman kube generate -f $fname $cname
-
-    # delete the container we generated from
-    run_podman rm -f $cname
+    fname="$PODMAN_TMPDIR/play_kube_wait_$(random_string 6).yaml"
+    echo "
+apiVersion: v1
+kind: Pod
+metadata:
+  labels:
+    app: test
+  name: test_pod
+spec:
+  restartPolicy: Never
+  containers:
+    - name: server
+      image: $IMAGE
+      command:
+      - top
+" > $fname
 
     # force a timeout to happen so that the kube play command is killed
     # and expect the timeout code 124 to happen so that we can clean up
     local t0=$SECONDS
-    PODMAN_TIMEOUT=15 run_podman 124 kube play --wait $fname
+    PODMAN_TIMEOUT=2 run_podman 124 kube play --wait $fname
     local t1=$SECONDS
     local delta_t=$((t1 - t0))
-    assert $delta_t -le 20 \
-           "podman kube play did not get killed within 10 seconds"
+    assert $delta_t -le 3 \
+           "podman kube play did not get killed within 3 seconds"
+    # Make sure we actually got SIGTERM and podman printed its message.
+    assert "$output" =~ "Cleaning up containers, pods, and volumes" "kube play printed sigterm message"
 
     # there should be no containers running or created
     run_podman ps -aq
@@ -656,7 +668,7 @@ EOF
 }
 
 @test "podman kube play --wait - wait for pod to exit" {
-    fname="/tmp/play_kube_wait_$(random_string 6).yaml"
+    fname="$PODMAN_TMPDIR/play_kube_wait_$(random_string 6).yaml"
     echo "
 apiVersion: v1
 kind: Pod
@@ -881,8 +893,7 @@ spec:
     done
     assert $output == "2-healthy" "After 3 seconds"
 
-    run_podman kube down $fname
-    run_podman pod rm -a
+    run_podman pod rm -fa -t0
     run_podman rm -a
 }
 
@@ -934,8 +945,7 @@ spec:
     done
     assert $output == "2-unhealthy" "After 3 seconds"
 
-    run_podman kube down $fname
-    run_podman pod rm -a
+    run_podman pod rm -fa -t0
     run_podman rm -a
 }