diff --git a/cmd/stdiscosrv/apisrv.go b/cmd/stdiscosrv/apisrv.go
index 36047a233..3a94dd3e9 100644
--- a/cmd/stdiscosrv/apisrv.go
+++ b/cmd/stdiscosrv/apisrv.go
@@ -67,7 +67,7 @@ type contextKey int
 
 const idKey contextKey = iota
 
-func newAPISrv(addr string, cert tls.Certificate, db database, repl replicator, useHTTP, compression bool, desiredNotFoundRate float64) *apiSrv {
+func newAPISrv(addr string, cert tls.Certificate, db database, repl replicator, useHTTP, compression bool, desiredUnseenNotFoundRate, desiredSeenNotFoundRate float64) *apiSrv {
 	return &apiSrv{
 		addr:        addr,
 		cert:        cert,
@@ -78,13 +78,13 @@ func newAPISrv(addr string, cert tls.Certificate, db database, repl replicator,
 		seenTracker: &retryAfterTracker{
 			name:         "seenTracker",
 			bucketStarts: time.Now(),
-			desiredRate:  desiredNotFoundRate / 2,
+			desiredRate:  desiredSeenNotFoundRate,
 			currentDelay: notFoundRetryUnknownMinSeconds,
 		},
 		notSeenTracker: &retryAfterTracker{
 			name:         "notSeenTracker",
 			bucketStarts: time.Now(),
-			desiredRate:  desiredNotFoundRate / 2,
+			desiredRate:  desiredUnseenNotFoundRate,
 			currentDelay: notFoundRetryUnknownMaxSeconds / 2,
 		},
 	}
@@ -564,5 +564,17 @@ func (t *retryAfterTracker) retryAfterS() int {
 	}
 	t.curCount++
 	t.mut.Unlock()
-	return t.currentDelay + rand.Intn(t.currentDelay/4)
+
+	// Skewed normal distribution with the mean at currentDelay and the
+	// limits (50% and 150%) at 3 standard deviations
+	nf := rand.NormFloat64()
+	minD := max(notFoundRetryUnknownMinSeconds, t.currentDelay/2)
+	maxD := min(notFoundRetryUnknownMaxSeconds, t.currentDelay*3/2)
+	intv := float64(maxD - t.currentDelay)
+	if nf < 0 {
+		intv = float64(t.currentDelay - minD)
+	}
+	nf = min(max(nf*intv/3+float64(t.currentDelay), notFoundRetryUnknownMinSeconds), notFoundRetryUnknownMaxSeconds)
+
+	return int(nf)
 }
diff --git a/cmd/stdiscosrv/apisrv_test.go b/cmd/stdiscosrv/apisrv_test.go
index 99f788763..54ea74ecd 100644
--- a/cmd/stdiscosrv/apisrv_test.go
+++ b/cmd/stdiscosrv/apisrv_test.go
@@ -18,6 +18,7 @@ import (
 	"regexp"
 	"strings"
 	"testing"
+	"time"
 
 	"github.com/syncthing/syncthing/lib/protocol"
 	"github.com/syncthing/syncthing/lib/tlsutil"
@@ -106,12 +107,59 @@ func addr(host string, port int) *net.TCPAddr {
 	}
 }
 
+func TestRetryAfterSHistogram(t *testing.T) {
+	tracker := &retryAfterTracker{
+		name:         "test",
+		bucketStarts: time.Now(),
+		desiredRate:  100,
+		currentDelay: 1800,
+	}
+
+	const n = 1000
+	bucketSize := 60 // seconds per histogram bucket
+	numBuckets := (notFoundRetryUnknownMaxSeconds + bucketSize - 1) / bucketSize
+	buckets := make([]int, numBuckets)
+
+	for i := 0; i < n; i++ {
+		v := tracker.retryAfterS()
+		if v < notFoundRetryUnknownMinSeconds || v > notFoundRetryUnknownMaxSeconds {
+			t.Fatalf("retryAfterS() = %d, out of range [%d, %d]", v, notFoundRetryUnknownMinSeconds, notFoundRetryUnknownMaxSeconds)
+		}
+		b := (v - 1) / bucketSize
+		if b >= numBuckets {
+			b = numBuckets - 1
+		}
+		buckets[b]++
+	}
+
+	// Print a horizontal histogram
+	maxCount := 0
+	for _, c := range buckets {
+		if c > maxCount {
+			maxCount = c
+		}
+	}
+	barWidth := 60
+	for i, c := range buckets {
+		lo := i*bucketSize + 1
+		hi := (i + 1) * bucketSize
+		if hi > notFoundRetryUnknownMaxSeconds {
+			hi = notFoundRetryUnknownMaxSeconds
+		}
+		bar := ""
+		if maxCount > 0 {
+			bar = strings.Repeat("#", c*barWidth/maxCount)
+		}
+		t.Logf("%4d-%4ds | %-*s %d", lo, hi, barWidth, bar, c)
+	}
+}
+
 func BenchmarkAPIRequests(b *testing.B) {
 	db := newInMemoryStore(b.TempDir(), 0, nil)
 	ctx, cancel := context.WithCancel(context.Background())
 	defer cancel()
 	go db.Serve(ctx)
-	api := newAPISrv("127.0.0.1:0", tls.Certificate{}, db, nil, true, true, 1000)
+	api := newAPISrv("127.0.0.1:0", tls.Certificate{}, db, nil, true, true, 1000, 1000)
 	srv := httptest.NewServer(http.HandlerFunc(api.handler))
 
 	kf := b.TempDir() + "/cert"
diff --git a/cmd/stdiscosrv/main.go b/cmd/stdiscosrv/main.go
index e6812cf43..2534c9be3 100644
--- a/cmd/stdiscosrv/main.go
+++ b/cmd/stdiscosrv/main.go
@@ -57,13 +57,16 @@ const (
 var debug = false
 
 type CLI struct {
-	Cert                string  `group:"Listen" help:"Certificate file" default:"./cert.pem" env:"DISCOVERY_CERT_FILE"`
-	Key                 string  `group:"Listen" help:"Key file" default:"./key.pem" env:"DISCOVERY_KEY_FILE"`
-	HTTP                bool    `group:"Listen" help:"Listen on HTTP (behind an HTTPS proxy)" env:"DISCOVERY_HTTP"`
-	Compression         bool    `group:"Listen" help:"Enable GZIP compression of responses" env:"DISCOVERY_COMPRESSION"`
-	Listen              string  `group:"Listen" help:"Listen address" default:":8443" env:"DISCOVERY_LISTEN"`
-	MetricsListen       string  `group:"Listen" help:"Metrics listen address" env:"DISCOVERY_METRICS_LISTEN"`
-	DesiredNotFoundRate float64 `group:"Listen" help:"Desired maximum rate of not-found replies (/s)" default:"1000"`
+	Cert                      string  `group:"Listen" help:"Certificate file" default:"./cert.pem" env:"DISCOVERY_CERT_FILE"`
+	Key                       string  `group:"Listen" help:"Key file" default:"./key.pem" env:"DISCOVERY_KEY_FILE"`
+	HTTP                      bool    `group:"Listen" help:"Listen on HTTP (behind an HTTPS proxy)" env:"DISCOVERY_HTTP"`
+	Compression               bool    `group:"Listen" help:"Enable GZIP compression of responses" env:"DISCOVERY_COMPRESSION"`
+	Listen                    string  `group:"Listen" help:"Listen address" default:":8443" env:"DISCOVERY_LISTEN"`
+	MetricsListen             string  `group:"Listen" help:"Metrics listen address" env:"DISCOVERY_METRICS_LISTEN"`
+	DesiredUnseenNotFoundRate float64 `group:"Listen" help:"Desired maximum rate of not-found replies for never seen devices (/s)" default:"1000" env:"DISCOVERY_UNSEEN_RATE"`
+	DesiredSeenNotFoundRate   float64 `group:"Listen" help:"Desired maximum rate of not-found replies for previously seen devices (/s)" default:"1000" env:"DISCOVERY_SEEN_RATE"`
+
+	ShutdownDelay float64 `help:"Time to wait before shutdown after receiving a shutdown signal (s)" env:"DISCOVERY_SHUTDOWN_DELAY"`
 
 	DBDir           string        `group:"Database" help:"Database directory" default:"." env:"DISCOVERY_DB_DIR"`
 	DBFlushInterval time.Duration `group:"Database" help:"Interval between database flushes" default:"5m" env:"DISCOVERY_DB_FLUSH_INTERVAL"`
@@ -145,7 +148,7 @@ func main() {
 	}
 
 	// Start the main API server.
-	qs := newAPISrv(cli.Listen, cert, db, repl, cli.HTTP, cli.Compression, cli.DesiredNotFoundRate)
+	qs := newAPISrv(cli.Listen, cert, db, repl, cli.HTTP, cli.Compression, cli.DesiredUnseenNotFoundRate, cli.DesiredSeenNotFoundRate)
 	main.Add(qs)
 
 	// If we have a metrics port configured, start a metrics handler.
@@ -167,7 +170,8 @@ func main() {
 	signal.Notify(signalChan, os.Interrupt)
 	go func() {
 		sig := <-signalChan
-		slog.Info("Received signal; shutting down", "signal", sig)
+		slog.Info("Received signal; shutting down", "signal", sig, "delay", cli.ShutdownDelay)
+		time.Sleep(time.Duration(float64(time.Second) * cli.ShutdownDelay))
 		cancel()
 	}()