diff --git a/pageserver/src/tenant/secondary/downloader.rs b/pageserver/src/tenant/secondary/downloader.rs
index 8a987b5ade..fb8907b5a8 100644
--- a/pageserver/src/tenant/secondary/downloader.rs
+++ b/pageserver/src/tenant/secondary/downloader.rs
@@ -31,7 +31,10 @@ use crate::{
 
 use super::{
     heatmap::HeatMapLayer,
-    scheduler::{self, Completion, JobGenerator, SchedulingResult, TenantBackgroundJobs},
+    scheduler::{
+        self, period_jitter, period_warmup, Completion, JobGenerator, SchedulingResult,
+        TenantBackgroundJobs,
+    },
     SecondaryTenant,
 };
 
@@ -45,7 +48,6 @@ use chrono::format::{DelayedFormat, StrftimeItems};
 use futures::Future;
 use pageserver_api::models::SecondaryProgress;
 use pageserver_api::shard::TenantShardId;
-use rand::Rng;
 use remote_storage::{DownloadError, Etag, GenericRemoteStorage};
 
 use tokio_util::sync::CancellationToken;
@@ -274,7 +276,7 @@ impl JobGenerator<PendingDownload, RunningDownload, CompleteDownload, DownloadCo
         // Update freshened_at even if there was an error: we don't want errored tenants to implicitly
         // take priority to run again.
         let mut detail = secondary_state.detail.lock().unwrap();
-        detail.next_download = Some(Instant::now() + DOWNLOAD_FRESHEN_INTERVAL);
+        detail.next_download = Some(Instant::now() + period_jitter(DOWNLOAD_FRESHEN_INTERVAL, 5));
     }
 
     async fn schedule(&mut self) -> SchedulingResult<PendingDownload> {
@@ -305,11 +307,9 @@ impl JobGenerator<PendingDownload, RunningDownload, CompleteDownload, DownloadCo
                     }
 
                     if detail.next_download.is_none() {
-                        // Initialize with a jitter: this spreads initial downloads on startup
-                        // or mass-attach across our freshen interval.
-                        let jittered_period =
-                            rand::thread_rng().gen_range(Duration::ZERO..DOWNLOAD_FRESHEN_INTERVAL);
-                        detail.next_download = Some(now.checked_add(jittered_period).expect(
+                        // Initialize randomly in the range from 0 to our interval: this uniformly spreads the start times.  Subsequent
+                        // rounds will use a smaller jitter to avoid accidentally synchronizing later.
+                        detail.next_download = Some(now.checked_add(period_warmup(DOWNLOAD_FRESHEN_INTERVAL)).expect(
                         "Using our constant, which is known to be small compared with clock range",
                     ));
                     }
diff --git a/pageserver/src/tenant/secondary/heatmap_uploader.rs b/pageserver/src/tenant/secondary/heatmap_uploader.rs
index 39d088ffc3..352409f5fc 100644
--- a/pageserver/src/tenant/secondary/heatmap_uploader.rs
+++ b/pageserver/src/tenant/secondary/heatmap_uploader.rs
@@ -20,12 +20,14 @@ use crate::{
 
 use futures::Future;
 use pageserver_api::shard::TenantShardId;
-use rand::Rng;
 use remote_storage::{GenericRemoteStorage, TimeoutOrCancel};
 
 use super::{
     heatmap::HeatMapTenant,
-    scheduler::{self, JobGenerator, RunningJob, SchedulingResult, TenantBackgroundJobs},
+    scheduler::{
+        self, period_jitter, period_warmup, JobGenerator, RunningJob, SchedulingResult,
+        TenantBackgroundJobs,
+    },
     CommandRequest, UploadCommand,
 };
 use tokio_util::sync::CancellationToken;
@@ -181,15 +183,11 @@ impl JobGenerator<UploadPending, WriteInProgress, WriteComplete, UploadCommand>
             let state = self
                 .tenants
                 .entry(*tenant.get_tenant_shard_id())
-                .or_insert_with(|| {
-                    let jittered_period = rand::thread_rng().gen_range(Duration::ZERO..period);
-
-                    UploaderTenantState {
-                        tenant: Arc::downgrade(&tenant),
-                        last_upload: None,
-                        next_upload: Some(now.checked_add(jittered_period).unwrap_or(now)),
-                        last_digest: None,
-                    }
+                .or_insert_with(|| UploaderTenantState {
+                    tenant: Arc::downgrade(&tenant),
+                    last_upload: None,
+                    next_upload: Some(now.checked_add(period_warmup(period)).unwrap_or(now)),
+                    last_digest: None,
                 });
 
             // Decline to do the upload if insufficient time has passed
@@ -274,7 +272,7 @@ impl JobGenerator<UploadPending, WriteInProgress, WriteComplete, UploadCommand>
 
             let next_upload = tenant
                 .get_heatmap_period()
-                .and_then(|period| now.checked_add(period));
+                .and_then(|period| now.checked_add(period_jitter(period, 5)));
 
             WriteComplete {
                     tenant_shard_id: *tenant.get_tenant_shard_id(),
diff --git a/pageserver/src/tenant/secondary/scheduler.rs b/pageserver/src/tenant/secondary/scheduler.rs
index 3bd7be782e..3d042f4513 100644
--- a/pageserver/src/tenant/secondary/scheduler.rs
+++ b/pageserver/src/tenant/secondary/scheduler.rs
@@ -1,4 +1,5 @@
 use futures::Future;
+use rand::Rng;
 use std::{
     collections::HashMap,
     marker::PhantomData,
@@ -19,6 +20,26 @@ use super::{CommandRequest, CommandResponse};
 const MAX_SCHEDULING_INTERVAL: Duration = Duration::from_secs(10);
 const MIN_SCHEDULING_INTERVAL: Duration = Duration::from_secs(1);
 
+/// Jitter a Duration by an integer percentage.  Returned values are uniform
+/// in the range 100-pct..100+pct (i.e. a 5% jitter is 5% either way: a ~10% range)
+pub(super) fn period_jitter(d: Duration, pct: u32) -> Duration {
+    if d == Duration::ZERO {
+        d
+    } else {
+        rand::thread_rng().gen_range((d * (100 - pct)) / 100..(d * (100 + pct)) / 100)
+    }
+}
+
+/// When a periodic task first starts, it should wait for some time in the range 0..period, so
+/// that starting many such tasks at the same time spreads them across the time range.
+pub(super) fn period_warmup(period: Duration) -> Duration {
+    if period == Duration::ZERO {
+        period
+    } else {
+        rand::thread_rng().gen_range(Duration::ZERO..period)
+    }
+}
+
 /// Scheduling helper for background work across many tenants.
 ///
 /// Systems that need to run background work across many tenants may use this type