diff --git a/pageserver/src/tenant/tasks.rs b/pageserver/src/tenant/tasks.rs
index f419d2e73a..eb77f7c83a 100644
--- a/pageserver/src/tenant/tasks.rs
+++ b/pageserver/src/tenant/tasks.rs
@@ -162,8 +162,11 @@ async fn compaction_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
 
             // TODO: we shouldn't need to await to find tenant and this could be moved outside of
             // loop, #3501. There are also additional "allowed_errors" in tests.
-            if first && random_init_delay(period, &cancel).await.is_err() {
-                break;
+            if first {
+                first = false;
+                if random_init_delay(period, &cancel).await.is_err() {
+                    break;
+                }
             }
 
             let started_at = Instant::now();
@@ -193,16 +196,7 @@ async fn compaction_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
                 }
             };
 
-            if !first {
-                // The first iteration is typically much slower, because all tenants compete for the
-                // compaction sempahore to run, and because of concurrent startup work like initializing
-                // logical sizes.  To avoid routinely spamming warnings, we suppress this log on first iteration.
-                warn_when_period_overrun(
-                    started_at.elapsed(),
-                    period,
-                    BackgroundLoopKind::Compaction,
-                );
-            }
+            warn_when_period_overrun(started_at.elapsed(), period, BackgroundLoopKind::Compaction);
 
             // Sleep
             if tokio::time::timeout(sleep_duration, cancel.cancelled())
@@ -211,8 +205,6 @@ async fn compaction_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
             {
                 break;
             }
-
-            first = false;
         }
     }
     .await;
@@ -247,8 +239,11 @@ async fn gc_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
 
             let period = tenant.get_gc_period();
 
-            if first && random_init_delay(period, &cancel).await.is_err() {
-                break;
+            if first {
+                first = false;
+                if random_init_delay(period, &cancel).await.is_err() {
+                    break;
+                }
             }
 
             let started_at = Instant::now();
@@ -282,12 +277,7 @@ async fn gc_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
                 }
             };
 
-            if !first {
-                // The first iteration is typically much slower, because all tenants compete for the
-                // compaction sempahore to run, and because of concurrent startup work like initializing
-                // logical sizes.  To avoid routinely spamming warnings, we suppress this log on first iteration.
-                warn_when_period_overrun(started_at.elapsed(), period, BackgroundLoopKind::Gc);
-            }
+            warn_when_period_overrun(started_at.elapsed(), period, BackgroundLoopKind::Gc);
 
             // Sleep
             if tokio::time::timeout(sleep_duration, cancel.cancelled())
@@ -296,8 +286,6 @@ async fn gc_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
             {
                 break;
             }
-
-            first = false;
         }
     }
     .await;
@@ -373,7 +361,7 @@ pub(crate) fn warn_when_period_overrun(
         // humantime does no significant digits clamping whereas Duration's debug is a bit more
         // intelligent. however it makes sense to keep the "configuration format" for period, even
         // though there's no way to output the actual config value.
-        warn!(
+        info!(
             ?elapsed,
             period = %humantime::format_duration(period),
             ?task,