diff --git a/internal/agent/agent.go b/internal/agent/agent.go
index 416d1b6..c49c539 100644
--- a/internal/agent/agent.go
+++ b/internal/agent/agent.go
@@ -380,7 +380,20 @@ func (a *Agent) NotComposed(ctx context.Context, why string) {
 // writeHave writes a module's have; on a node composing its own, with the sealed values of the composition it names
 // when the caller gave none (Have.Sealed): those of the composition the agent applied or holds at that digest, else
 // those the module's last have said at that digest.
+//
+// A writer that names no composition (one written from the agent's running entry before this agent ran anything of the
+// module since its start: held by a failed backup, waiting for a yes, not composed) keeps what the module's last have
+// said runs, its fingerprint, digest and sealed values, rather than a have naming nothing: what runs is not lost, and
+// the boxes the composer reuses after a restart stay (review of L2, rounds 2 and 3).
 func (a *Agent) writeHave(ctx context.Context, h Have) {
+	if h.Composed == "" && h.Module != NodeModule {
+		if last, ok := a.env.Haves.Read(ctx, h.Module); ok && last.Composed != "" {
+			h.FP, h.Composed = last.FP, last.Composed
+			if h.Sealed == nil {
+				h.Sealed = last.Sealed
+			}
+		}
+	}
 	if a.env.SelfComposed && h.Sealed == nil && h.Module != NodeModule && h.Composed != "" {
 		h.Sealed = a.sealedOf(ctx, h.Module, h.FP, h.Composed)
 	}
@@ -1100,6 +1113,17 @@ func (a *Agent) waitsForYes(ctx context.Context, module string, w wantNow, comp
 	from, known := a.runningComposition(module)
 	prior := ran || a.prior[module]
 	a.mu.Unlock()
+	if !ran && !known {
+		// Nothing of it run since this agent's start, and no kept declaration: its last have says what runs (review of L2,
+		// round 3). The same composition is no move; another one is a move whose source cannot be read, so it waits for
+		// a yes rather than being taken as the module's first composition.
+		if h, ok := a.env.Haves.Read(ctx, module); ok && h.Composed != "" {
+			if h.Composed == comp.Dig {
+				return false
+			}
+			prior = true
+		}
+	}
 	var j delivery.Judged
 	switch {
 	case known:
diff --git a/internal/agent/agent_test.go b/internal/agent/agent_test.go
index a2d7a15..44290f5 100644
--- a/internal/agent/agent_test.go
+++ b/internal/agent/agent_test.go
@@ -965,7 +965,7 @@ func TestTheNodesOwnCompositionIsAppliedWhenItDiffersAndARecordMoveWaitsForAYes(
 	b := newBed(t)
 	b.env.SelfComposed, b.env.Trusted = true, nil
 	b.env.Policy = func(m string) string {
-		if m == "db" {
+		if m == "db" || m == "rec" {
 			return catalogue.PolicyRecord
 		}
 		return catalogue.PolicyRoll
@@ -1039,7 +1039,8 @@ func TestTheNodesOwnCompositionIsAppliedWhenItDiffersAndARecordMoveWaitsForAYes(
 
 	// A record module: its first composition is no move; a new image recreates its container and waits for a yes.
 	container := func(image string) json.RawMessage {
-		raw, _ := json.Marshal(map[string]any{"id": "db.server", "type": "container", "module": "db", "name": "db", "image": image})
+		module := strings.SplitN(image, "@", 2)[0]
+		raw, _ := json.Marshal(map[string]any{"id": module + ".server", "type": "container", "module": module, "name": module, "image": image})
 		return raw
 	}
 	dk, draw, _ := unsigned("db", fp, container("db@sha256:"+strings.Repeat("1", 64)))
@@ -1048,18 +1049,40 @@ func TestTheNodesOwnCompositionIsAppliedWhenItDiffersAndARecordMoveWaitsForAYes(
 	eventually(t, "the record module's first composition was not applied", func() bool { return len(b.appliedList()) == 3 })
 	fpB := fpOf("b")
 	dk2, draw2, ddig2 := unsigned("db", fpB, container("db@sha256:"+strings.Repeat("2", 64)))
+	// rec is a record module this agent has run nothing of since its start (the switch and every delivery of the
+	// node-engine restart it): its have alone says what runs. Its move waits for a yes as db's does, and its have keeps
+	// what runs (fingerprint, digest, sealed values) rather than naming nothing (review of L2, round 3).
+	recFP, recDig := fpOf("d"), "sha256:"+strings.Repeat("8", 64)
+	b.haves.Write(context.Background(), Have{Module: "rec", FP: recFP, Composed: recDig, Phase: string(delivery.PhaseRunning),
+		Sealed: []string{`{"box":"rec"}`}})
+	rk, rraw, rdig := unsigned("rec", fpB, container("rec@sha256:"+strings.Repeat("3", 64)))
 	b.comps.put(dk2, draw2)
+	b.comps.put(rk, rraw)
 	want("db", fpB, "")
-	eventually(t, "the move did not wait for a yes", func() bool {
-		h := b.haves.last("db")
-		return h.Phase == string(delivery.PhaseWaitingYes) && h.Judgement == string(delivery.JudgedRecreates) && h.Waits == ddig2
-	})
-	if got := b.appliedList(); len(got) != 3 {
+	want("rec", fpB, "")
+	applied := len(b.appliedList())
+	for _, row := range []struct {
+		module, fp, composed, waits string
+		sealed                      []string
+	}{{"db", fp, "", ddig2, nil}, {"rec", recFP, recDig, rdig, []string{`{"box":"rec"}`}}} {
+		eventually(t, row.module+"'s move did not wait for a yes", func() bool {
+			h := b.haves.last(row.module)
+			return h.Phase == string(delivery.PhaseWaitingYes) && h.Waits == row.waits
+		})
+		h := b.haves.last(row.module)
+		if h.FP != row.fp || (row.composed != "" && h.Composed != row.composed) || h.Composed == "" ||
+			(row.sealed != nil && !slices.Equal(h.Sealed, row.sealed)) {
+			t.Errorf("%s's have waiting for a yes does not keep what runs: %+v", row.module, h)
+		}
+	}
+	if got := b.appliedList(); len(got) != applied {
 		t.Fatalf("a move waiting for a yes was applied: %v", got)
 	}
 	want("db", fpB, ddig2)
+	want("rec", fpB, rdig)
 	eventually(t, "the yes did not apply the move", func() bool {
-		h := b.haves.last("db")
-		return len(b.appliedList()) == 4 && h.Phase == string(delivery.PhaseRunning) && h.FP == fpB
+		h, r := b.haves.last("db"), b.haves.last("rec")
+		return len(b.appliedList()) == applied+2 && h.Phase == string(delivery.PhaseRunning) && h.FP == fpB &&
+			r.Phase == string(delivery.PhaseRunning) && r.FP == fpB && r.Composed == rdig
 	})
 }