diff --git a/pageserver/src/tenant/timeline/eviction_task.rs b/pageserver/src/tenant/timeline/eviction_task.rs
index 5485cc42b4..354f971e11 100644
--- a/pageserver/src/tenant/timeline/eviction_task.rs
+++ b/pageserver/src/tenant/timeline/eviction_task.rs
@@ -308,8 +308,13 @@ impl Timeline {
         ctx: &RequestContext,
     ) -> ControlFlow<()> {
         let mut state = self.eviction_task_timeline_state.lock().await;
+
+        // Only do the imitate_layer accesses approximately as often as the threshold.  A little
+        // more frequently, to avoid this period racing with the threshold/period-th eviction iteration.
+        let inter_imitate_period = p.threshold.checked_sub(p.period).unwrap_or(p.threshold);
+
         match state.last_layer_access_imitation {
-            Some(ts) if ts.elapsed() < p.threshold => { /* no need to run */ }
+            Some(ts) if ts.elapsed() < inter_imitate_period => { /* no need to run */ }
             _ => {
                 self.imitate_timeline_cached_layer_accesses(cancel, ctx)
                     .await;
@@ -332,7 +337,7 @@ impl Timeline {
         };
         let mut state = tenant.eviction_task_tenant_state.lock().await;
         match state.last_layer_access_imitation {
-            Some(ts) if ts.elapsed() < p.threshold => { /* no need to run */ }
+            Some(ts) if ts.elapsed() < inter_imitate_period => { /* no need to run */ }
             _ => {
                 self.imitate_synthetic_size_calculation_worker(&tenant, ctx, cancel)
                     .await;