diff --git a/acceptance/cluster/localcluster.go b/acceptance/cluster/localcluster.go
index 29fe34484fb6..ccca4ab86a31 100644
--- a/acceptance/cluster/localcluster.go
+++ b/acceptance/cluster/localcluster.go
@@ -225,7 +225,13 @@ func (l *LocalCluster) OneShot(
 	if err := l.oneshot.Start(); err != nil {
 		return err
 	}
-	return l.oneshot.Wait()
+	err = l.oneshot.Wait()
+	if err != nil {
+		var b bytes.Buffer
+		l.oneshot.Logs(&b)
+		return fmt.Errorf("%s:\n%s", err, b.String())
+	}
+	return nil
 }
 
 // stopOnPanic is invoked as a deferred function in Start in order to attempt
diff --git a/acceptance/reference_test.go b/acceptance/reference_test.go
index 7f4165eab1bd..95ab4b47f669 100644
--- a/acceptance/reference_test.go
+++ b/acceptance/reference_test.go
@@ -21,14 +21,26 @@ import (
 	"testing"
 )
 
+func runReferenceTestWithScript(
+	t *testing.T,
+	script string,
+) {
+	if err := testDockerOneShot(t, "reference", []string{"/cockroach", "version"}); err != nil {
+		t.Skipf(`TODO(dt): No /cockroach binary in one-shot container, see #6086: %s`, err)
+	}
+
+	err := testDockerOneShot(t, "reference", []string{"/bin/bash", "-c", script})
+	if err != nil {
+		t.Errorf("expected success: %s", err)
+	}
+
+}
+
 func runReadWriteReferenceTest(
 	t *testing.T,
 	referenceBinPath string,
 	backwardReferenceTest string,
 ) {
-	if err := testDockerSingleNode(t, "reference", []string{"/cockroach", "version"}); err != nil {
-		t.Skipf(`TODO(dt): No /cockroach binary in one-shot container, see #6086: %s`, err)
-	}
 	referenceTestScript := fmt.Sprintf(`
 set -xe
 mkdir /old
@@ -41,6 +53,7 @@ bin=/%s/cockroach
 # TODO(bdarnell): when --background is in referenceBinPath, use it here and below.
 $bin start &
 sleep 1
+
 echo "Use the reference binary to write a couple rows, then render its output to a file and shut down."
 $bin sql -e "CREATE DATABASE old"
 $bin sql -d old -e "CREATE TABLE testing_old (i int primary key, b bool, s string unique, d decimal, f float, t timestamp, v interval, index sb (s, b))"
@@ -56,6 +69,10 @@ $bin sql -d old -e "SELECT i, b, s, d, f, v, extract(epoch FROM t) FROM testing_
 # diff returns non-zero if different. With set -e above, that would exit here.
 diff new.everything old.everything
 
+# Scan all data (some of which may not have been touched by the SQL commands)
+# to wake up all Raft groups.
+$bin debug kv scan
+
 echo "Add a row with the new binary and render the updated data before shutting down."
 $bin sql -d old -e "INSERT INTO testing_old values (3, false, '!', decimal '2.14159', 2.14159, NOW(), interval '3h')"
 $bin sql -d old -e "SELECT i, b, s, d, f, v, extract(epoch FROM t) FROM testing_old" > new.everything
@@ -70,10 +87,7 @@ echo "Read the modified data using the reference binary again."
 bin=/%s/cockroach
 %s
 `, referenceBinPath, referenceBinPath, backwardReferenceTest)
-	err := testDockerSingleNode(t, "reference", []string{"/bin/bash", "-c", referenceTestScript})
-	if err != nil {
-		t.Errorf("expected success: %s", err)
-	}
+	runReferenceTestWithScript(t, referenceTestScript)
 }
 
 func TestDockerReadWriteBidirectionalReferenceVersion(t *testing.T) {
@@ -98,3 +112,23 @@ $bin quit && wait
 `
 	runReadWriteReferenceTest(t, `forward-reference-version`, backwardReferenceTest)
 }
+
+func TestDockerMigration_7429(t *testing.T) {
+	script := `
+set -eux
+bin=/cockroach
+
+touch out
+
+function finish {
+  cat out
+}
+
+trap finish EXIT
+
+$bin start --alsologtostderr=INFO --background --store=/cockroach-data-reference-7429 &> out
+$bin debug kv scan
+$bin quit
+`
+	runReferenceTestWithScript(t, script)
+}
diff --git a/acceptance/replication_test.go b/acceptance/replication_test.go
index 06c9c5b046ac..11460e04ba82 100644
--- a/acceptance/replication_test.go
+++ b/acceptance/replication_test.go
@@ -38,6 +38,12 @@ func countRangeReplicas(db *client.DB) (int, error) {
 }
 
 func checkRangeReplication(t *testing.T, c cluster.Cluster, d time.Duration) {
+	if c.NumNodes() < 1 {
+		// Looks silly, but we actually start zero-node clusters in the
+		// reference tests.
+		t.Log("replication test is a no-op for empty cluster")
+		return
+	}
 	// Always talk to node 0.
 	client, dbStopper := c.NewClient(t, 0)
 	defer dbStopper.Stop()
diff --git a/acceptance/util_test.go b/acceptance/util_test.go
index 47a77b1ee663..1309021eb5d6 100644
--- a/acceptance/util_test.go
+++ b/acceptance/util_test.go
@@ -208,11 +208,17 @@ func StartCluster(t *testing.T, cfg cluster.TestConfig) (c cluster.Cluster) {
 	if !*flagRemote {
 		logDir := *flagLogDir
 		if logDir != "" {
-			_, _, fun := caller.Lookup(3)
-			if !testFuncRE.MatchString(fun) {
-				t.Fatalf("invalid caller %s; want TestX -> runTestOnConfigs -> func()", fun)
+			var i int
+			for ; i < 100; i++ {
+				_, _, fun := caller.Lookup(i)
+				if testFuncRE.MatchString(fun) {
+				}
+				logDir = filepath.Join(logDir, fun)
+				break
+			}
+			if i >= 100 {
+				panic("no caller matching Test(.*) in stack trace")
 			}
-			logDir = filepath.Join(logDir, fun)
 		}
 		l := cluster.CreateLocal(cfg, logDir, *flagPrivileged, stopper)
 		l.Start()
@@ -279,18 +285,18 @@ const (
 	postgresTestImage = "cockroachdb/postgres-test:" + postgresTestTag
 )
 
-func testDockerSingleNode(t *testing.T, name string, cmd []string) error {
+func testDocker(t *testing.T, num int, name string, cmd []string) error {
 	SkipUnlessLocal(t)
 	cfg := cluster.TestConfig{
 		Name:     name,
 		Duration: *flagDuration,
-		Nodes:    []cluster.NodeConfig{{Count: 1, Stores: []cluster.StoreConfig{{Count: 1}}}},
+		Nodes:    []cluster.NodeConfig{{Count: int32(num), Stores: []cluster.StoreConfig{{Count: 1}}}},
 	}
 	l := StartCluster(t, cfg).(*cluster.LocalCluster)
 	defer l.AssertAndStop(t)
 
 	containerConfig := container.Config{
-		Image: fmt.Sprintf(postgresTestImage),
+		Image: postgresTestImage,
 		Env: []string{
 			"PGHOST=roach0",
 			fmt.Sprintf("PGPORT=%s", base.DefaultPort),
@@ -302,3 +308,11 @@ func testDockerSingleNode(t *testing.T, name string, cmd []string) error {
 	hostConfig := container.HostConfig{NetworkMode: "host"}
 	return l.OneShot(postgresTestImage, types.ImagePullOptions{}, containerConfig, hostConfig, "docker-"+name)
 }
+
+func testDockerSingleNode(t *testing.T, name string, cmd []string) error {
+	return testDocker(t, 1, name, cmd)
+}
+
+func testDockerOneShot(t *testing.T, name string, cmd []string) error {
+	return testDocker(t, 0, name, cmd)
+}