diff --git a/test/e2e/manifest_test.go b/test/e2e/manifest_test.go
index 6ae73ba2a5..02f57d0f93 100644
--- a/test/e2e/manifest_test.go
+++ b/test/e2e/manifest_test.go
@@ -597,7 +597,8 @@ RUN touch /file
 
 		push := podmanTest.Podman([]string{"push", "-q", "--tls-verify=false", "--creds=" + registry.User + ":" + registry.Password, "--format=v2s2", "localhost:" + registry.Port + "/citest:latest"})
 		push.WaitWithDefaultTimeout()
-		Expect(push).Should(ExitCleanly())
+		// Cannot ExitCleanly() because this sometimes warns "Failed, retrying in 1s"
+		Expect(push).Should(Exit(0))
 
 		session = podmanTest.Podman([]string{"manifest", "add", "--tls-verify=false", "--creds=" + registry.User + ":" + registry.Password, "foo", "localhost:" + registry.Port + "/citest:latest"})
 		session.WaitWithDefaultTimeout()
diff --git a/test/system/520-checkpoint.bats b/test/system/520-checkpoint.bats
index a43cf89a94..31b5b9af0c 100644
--- a/test/system/520-checkpoint.bats
+++ b/test/system/520-checkpoint.bats
@@ -67,13 +67,19 @@ function teardown() {
     is "$output" "running:true:false:false" \
        "State. Status:Running:Pause:Checkpointed"
 
-    # Pause briefly to let restarted container emit some output
-    sleep 0.3
-
-    # Get full logs, and make sure something changed
-    run_podman logs $cid
-    local nlines_after="${#lines[*]}"
-    assert $nlines_after -gt $nlines_before \
+    # Re-fetch logs, and ensure that they continue growing.
+    # Allow a short while for container process to actually restart.
+    local retries=10
+    while [[ $retries -gt 0 ]]; do
+        run_podman logs $cid
+        local nlines_after="${#lines[*]}"
+        if [[ $nlines_after -gt $nlines_before ]]; then
+            break
+        fi
+        sleep 0.1
+        retries=$((retries - 1))
+    done
+    assert "$retries" -gt 0 \
            "Container failed to output new lines after first restore"
 
     # Same thing again: test for https://github.com/containers/crun/issues/756
@@ -83,12 +89,18 @@ function teardown() {
     nlines_before="${#lines[*]}"
     run_podman container restore $cid
 
-    # Give container time to write new output; then confirm that something
-    # was emitted
-    sleep 0.3
-    run_podman container logs $cid
-    nlines_after="${#lines[*]}"
-    assert $nlines_after -gt $nlines_before \
+    # Same as above, confirm that we get new output
+    retries=10
+    while [[ $retries -gt 0 ]]; do
+        run_podman logs $cid
+        local nlines_after="${#lines[*]}"
+        if [[ $nlines_after -gt $nlines_before ]]; then
+            break
+        fi
+        sleep 0.1
+        retries=$((retries - 1))
+    done
+    assert "$retries" -gt 0 \
            "stdout went away after second restore (crun issue 756)"
 
     run_podman rm -t 0 -f $cid
diff --git a/test/system/700-play.bats b/test/system/700-play.bats
index 0f302400dd..3720bff495 100644
--- a/test/system/700-play.bats
+++ b/test/system/700-play.bats
@@ -769,9 +769,16 @@ EOF
     CONTAINERS_CONF_OVERRIDE="$containersConf" run_podman kube play $YAML
     run_podman container inspect --format '{{ .Config.Umask }}' $ctrInPod
     is "${output}" "0472"
-    # Confirm that umask actually takes effect
-    run_podman logs $ctrInPod
-    is "$output" "204" "stat() on created file"
+    # Confirm that umask actually takes effect. Might take a second or so.
+    local retries=10
+    while [[ $retries -gt 0 ]]; do
+        run_podman logs $ctrInPod
+        test -n "$output" && break
+        sleep 0.1
+        retries=$((retries - 1))
+    done
+    assert "$retries" -gt 0 "Timed out waiting for container output"
+    assert "$output" = "204" "stat() on created file"
 
     run_podman kube down $YAML
     run_podman pod rm -a