diff --git a/daemon/daemon.go b/daemon/daemon.go
index 2da69bc..144d0c4 100644
--- a/daemon/daemon.go
+++ b/daemon/daemon.go
@@ -3,6 +3,7 @@ package daemon
 import (
 	"context"
 	"fmt"
+	"math/rand"
 	"os"
 	"os/signal"
 	"strings"
@@ -38,6 +39,12 @@ func Run(ctx context.Context, conf *config.Config) error {
 		cancel()
 	}()
 
+	// The math/rand package is used presently for generating trace IDs, we
+	// seed it with the current time and pid so that the IDs are mostly
+	// unique.
+	rand.Seed(time.Now().UnixNano())
+	rand.Seed(int64(os.Getpid()))
+
 	outlets, err := logging.OutletsFromConfig(*conf.Global.Logging)
 	if err != nil {
 		return errors.Wrap(err, "cannot build logging from config")
diff --git a/daemon/logging/trace/trace_genID.go b/daemon/logging/trace/trace_genID.go
index 0fcd043..908e3bd 100644
--- a/daemon/logging/trace/trace_genID.go
+++ b/daemon/logging/trace/trace_genID.go
@@ -3,20 +3,11 @@ package trace
 import (
 	"encoding/base64"
 	"math/rand"
-	"os"
 	"strings"
-	"time"
 
 	"github.com/zrepl/zrepl/util/envconst"
 )
 
-var genIdPRNG = rand.New(rand.NewSource(1))
-
-func init() {
-	genIdPRNG.Seed(time.Now().UnixNano())
-	genIdPRNG.Seed(int64(os.Getpid()))
-}
-
 var genIdNumBytes = envconst.Int("ZREPL_TRACE_ID_NUM_BYTES", 3)
 
 func init() {
@@ -30,7 +21,7 @@ func genID() string {
 	enc := base64.NewEncoder(base64.RawStdEncoding, &out)
 	buf := make([]byte, genIdNumBytes)
 	for i := 0; i < len(buf); {
-		n, err := genIdPRNG.Read(buf[i:])
+		n, err := rand.Read(buf[i:])
 		if err != nil {
 			panic(err)
 		}