diff --git a/internal/proxy/udprelay/run.go b/internal/proxy/udprelay/run.go
index 1d80a8e..a7395a5 100644
--- a/internal/proxy/udprelay/run.go
+++ b/internal/proxy/udprelay/run.go
@@ -51,6 +51,7 @@ type Deps struct {
 	ConnectedStreams *atomic.Int32
 	OnTURNServer     func(ip net.IP)
 	fatalCh          chan error
+	allocPace        *allocPacer
 }
 
 func (d *Deps) log() logx.Logger {
@@ -91,6 +92,7 @@ func Run(ctx context.Context, dtlsDialer *dtlsdial.Dialer, auth AuthHandler, log
 		ConnectedStreams: connectedStreams,
 		OnTURNServer:     onTURNServer,
 		fatalCh:          fatalCh,
+		allocPace:        newAllocPacer(allocPaceInterval),
 	}
 
 	runCtx, runCancel := context.WithCancel(ctx)
@@ -105,6 +107,18 @@ func Run(ctx context.Context, dtlsDialer *dtlsdial.Dialer, auth AuthHandler, log
 		}
 	}()
 
+	var fatalErr atomic.Pointer[error]
+	watcherDone := make(chan struct{})
+	go func() {
+		defer close(watcherDone)
+		select {
+		case err := <-fatalCh:
+			fatalErr.Store(&err)
+			runCancel()
+		case <-runCtx.Done():
+		}
+	}()
+
 	inboundChan := make(chan *Packet, inboundQueueCap)
 	wg := sync.WaitGroup{}
 	wg.Go(deps.guard(func() {
@@ -140,18 +154,6 @@ func Run(ctx context.Context, dtlsDialer *dtlsdial.Dialer, auth AuthHandler, log
 		}))
 	}
 
-	var fatalErr atomic.Pointer[error]
-	watcherDone := make(chan struct{})
-	go func() {
-		defer close(watcherDone)
-		select {
-		case err := <-fatalCh:
-			fatalErr.Store(&err)
-			runCancel()
-		case <-runCtx.Done():
-		}
-	}()
-
 	wg.Wait()
 	runCancel()
 	<-deadlineSet
diff --git a/internal/proxy/udprelay/run_test.go b/internal/proxy/udprelay/run_test.go
index e116be5..909f721 100644
--- a/internal/proxy/udprelay/run_test.go
+++ b/internal/proxy/udprelay/run_test.go
@@ -119,3 +119,27 @@ func TestRunReturnsOnStreamPanic(t *testing.T) {
 		t.Fatal("Run hung on panic in stream goroutine")
 	}
 }
+
+func TestRunFatalDoesNotWaitWarmupBarrier(t *testing.T) {
+	t.Parallel()
+	dialer, params, peer, local := runFatalDeps(t)
+
+	var connected atomic.Int32
+	done := make(chan error, 1)
+	start := time.Now()
+	go func() {
+		done <- Run(context.Background(), dialer, stubAuth{}, logx.Nop(), &connected, nil, params, peer, local, 4)
+	}()
+
+	select {
+	case err := <-done:
+		if !errors.Is(err, ErrFatal) {
+			t.Fatalf("err = %v, want ErrFatal", err)
+		}
+		if elapsed := time.Since(start); elapsed >= streamStartBarrier {
+			t.Fatalf("Run took %v, want less than warm-up barrier %v", elapsed, streamStartBarrier)
+		}
+	case <-time.After(2 * streamStartBarrier):
+		t.Fatal("Run hung on fatal provider error")
+	}
+}