diff --git a/internal/streams/stream_provider_server_side.go b/internal/streams/stream_provider_server_side.go
index fa2696de..60d07677 100644
--- a/internal/streams/stream_provider_server_side.go
+++ b/internal/streams/stream_provider_server_side.go
@@ -2,7 +2,10 @@ package streams
 
 import (
 	"net/http"
+	"os"
+	"strconv"
 	"sync"
+	"time"
 
 	"github.com/launchdarkly/ld-relay/v8/internal/sdkauth"
 
@@ -109,6 +112,7 @@ func (r *serverSideEnvStreamRepository) Replay(channel, id string) chan eventsou
 // getReplayEvent will return a ServerSidePutEvent with all the data needed for a Replay.
 func (r *serverSideEnvStreamRepository) getReplayEvent() (eventsource.Event, error) {
 	data, err, _ := r.flightGroup.Do("getReplayEvent", func() (interface{}, error) {
+		start := time.Now()
 		flags, err := r.store.GetAll(ldstoreimpl.Features())
 
 		if err != nil {
@@ -126,7 +130,19 @@ func (r *serverSideEnvStreamRepository) getReplayEvent() (eventsource.Event, err
 			{Kind: ldstoreimpl.Segments(), Items: removeDeleted(segments)},
 		}
 
+		// This call uses a lot of system resources (RAM in particular).
 		event := MakeServerSidePutEvent(allData)
+		// So we sleep for a bit to allow a bunch of concurrent calls to
+		// all make use of this same flightGroup.
+		delayS := os.Getenv("LD_STREAMING_DELAY_SECONDS")
+		if delay, err := strconv.Atoi(delayS); err == nil {
+			if delay > 0 && delay <= 60 {
+				time.Sleep(time.Duration(delay)*time.Second - time.Since(start))
+			} else {
+				r.loggers.Warnf("Ignoring invalid value for LD_STREAMING_DELAY_SECONDS: %s", delayS)
+			}
+		}
+
 		return event, nil
 	})