diff --git a/test/system/035-logs.bats b/test/system/035-logs.bats
index 9868d4e3cf..e0d80db689 100644
--- a/test/system/035-logs.bats
+++ b/test/system/035-logs.bats
@@ -182,8 +182,10 @@ function _log_test_since() {
     before=$(date --iso-8601=seconds)
     run_podman run --log-driver=$driver -d --name test $IMAGE sh -c \
         "echo $s_before; trap 'echo $s_after; exit' SIGTERM; while :; do sleep 0.1; done"
+    wait_for_output "$s_before" test
 
     # sleep a second to make sure the date is after the first echo
+    # (We could instead use iso-8601=ns but seconds feels more real-world)
     sleep 1
     after=$(date --iso-8601=seconds)
     run_podman stop test
diff --git a/test/system/helpers.bash b/test/system/helpers.bash
index ded6de6425..dc5575e737 100644
--- a/test/system/helpers.bash
+++ b/test/system/helpers.bash
@@ -442,7 +442,7 @@ function run_podman() {
 
 # Wait for certain output from a container, indicating that it's ready.
 function wait_for_output {
-    local sleep_delay=5
+    local sleep_delay=1
     local how_long=$PODMAN_TIMEOUT
     local expect=
     local cid=