diff --git a/modules/brother/README.md b/modules/brother/README.md
index 50089e55..4183fa17 100644
--- a/modules/brother/README.md
+++ b/modules/brother/README.md
@@ -82,7 +82,7 @@ is not given, and the printer is not contacted.
 ### Documents in parts
 
 The bus refuses a message over 1 MiB, so a document crosses it in parts of at most 700 KiB (both the size this module
-cuts and the most it accepts; ADR 0468 clause 3 says 768 KiB, which is 1 MiB of base64 before the message around it),
+cuts and the most it accepts, as ADR 0468 clause 3 says),
 counted from 1, each carried base64-encoded in JSON. A caller joins the parts and checks the SHA-256. The bucket
 (`s3-bucket`, from `minio`) is spoken to by the device process alone, from `store.json` (owner `brother-device`, mode
 0600), with the S3 client mesh-mail uses; a scan is kept once as `<sha256>.pdf` and an upload as `uploads/<id>.<ext>`.
diff --git a/modules/brother/cmd/brother/admin_test.go b/modules/brother/cmd/brother/admin_test.go
index c78a61e1..f51f3465 100644
--- a/modules/brother/cmd/brother/admin_test.go
+++ b/modules/brother/cmd/brother/admin_test.go
@@ -119,6 +119,12 @@ func (f *fakePrinter) host() string { return strings.TrimPrefix(f.URL, "https://
 // print is the fingerprint of the certificate the server serves.
 func (f *fakePrinter) print() string { return Fingerprint(f.TLS.Certificates[0].Certificate[0]) }
 
+func (f *fakePrinter) connsNow() int {
+	f.mu.Lock()
+	defer f.mu.Unlock()
+	return f.conns
+}
+
 func (f *fakePrinter) loggedInNow() int {
 	f.mu.Lock()
 	defer f.mu.Unlock()
diff --git a/modules/brother/cmd/brother/parts.go b/modules/brother/cmd/brother/parts.go
index 114e5df0..df357ded 100644
--- a/modules/brother/cmd/brother/parts.go
+++ b/modules/brother/cmd/brother/parts.go
@@ -11,8 +11,7 @@ import (
 const (
 	// PartSize is how large the parts this module cuts are, and MaxPart the most raw bytes a part may hold; a part
 	// of more is refused. They are one: 700 KiB, so that a part's base64 text (about 933 KB) and the message around
-	// it stay under the bus's 1 MiB. (ADR 0468 clause 3 says at most 768 KiB, which is 1 MiB of base64 before the
-	// message around it, and so over the bus's limit.)
+	// it stay under the bus's 1 MiB. (ADR 0468 clause 3.)
 	PartSize = 700 << 10
 	MaxPart  = PartSize
 	// MostParts bounds how many parts one document has (a 100 MiB document is the most).
diff --git a/modules/brother/cmd/brother/printer_test.go b/modules/brother/cmd/brother/printer_test.go
index 45dad26c..fc73230d 100644
--- a/modules/brother/cmd/brother/printer_test.go
+++ b/modules/brother/cmd/brother/printer_test.go
@@ -119,8 +119,8 @@ func TestPrinterSettingsSaysWhichConfigIsUnsetAndQueuesNothing(t *testing.T) {
 			t.Errorf("%s: an ask was queued", c.name)
 		}
 	}
-	if f.conns != 0 || len(f.requests) != 0 {
-		t.Errorf("the printer was contacted: %d connections, %v", f.conns, f.requests)
+	if f.connsNow() != 0 || len(f.requests) != 0 {
+		t.Errorf("the printer was contacted: %d connections, %v", f.connsNow(), f.requests)
 	}
 }
 
@@ -141,8 +141,8 @@ func TestPrinterSettingsSaysTheSecretIsNotGivenAndContactsNothing(t *testing.T)
 	if _, err := r.run(nil); err == nil || !strings.Contains(err.Error(), "admin-password is not given") {
 		t.Errorf("empty secret: error = %v", err)
 	}
-	if f.conns != 0 || len(f.requests) != 0 {
-		t.Errorf("the printer was contacted: %d connections, %v", f.conns, f.requests)
+	if f.connsNow() != 0 || len(f.requests) != 0 {
+		t.Errorf("the printer was contacted: %d connections, %v", f.connsNow(), f.requests)
 	}
 }
 
@@ -162,8 +162,8 @@ func TestPrinterSettingsRefusesAPageOutsideTheSite(t *testing.T) {
 	if _, err := r.run(map[string]any{"page": 5}); err == nil {
 		t.Errorf("a page that is no string was accepted")
 	}
-	if r.bus.asks() != 0 || f.conns != 0 {
-		t.Errorf("%d asks queued, the printer contacted %d times", r.bus.asks(), f.conns)
+	if r.bus.asks() != 0 || f.connsNow() != 0 {
+		t.Errorf("%d asks queued, the printer contacted %d times", r.bus.asks(), f.connsNow())
 	}
 }
 
@@ -193,14 +193,14 @@ func TestTheAdminWorkerSettlesEachAsk(t *testing.T) {
 		t.Errorf("an unreadable ask: action %v, want term", act)
 	}
 	old, _ := json.Marshal(Ask{ID: "old", Op: OpSettings, Page: DefaultPage, At: fixedNow.Add(-StaleAfter - time.Second)})
-	if act, _ := w.Handle(old, nil); act != actionAck || r.answers.get("old") != nil || f.conns != 0 {
-		t.Errorf("a stale ask: action %v, answer %s, %d connections", act, r.answers.get("old"), f.conns)
+	if act, _ := w.Handle(old, nil); act != actionAck || r.answers.get("old") != nil || f.connsNow() != 0 {
+		t.Errorf("a stale ask: action %v, answer %s, %d connections", act, r.answers.get("old"), f.connsNow())
 	}
 	fresh, _ := json.Marshal(Ask{ID: "a1", Op: OpSettings, Page: DefaultPage, At: fixedNow})
 	if act, _ := w.Handle(fresh, nil); act != actionAck || r.answers.get("a1") == nil {
 		t.Errorf("a fresh ask: action %v", act)
 	}
-	conns := f.conns
+	conns := f.connsNow()
 	if act, _ := w.Handle(fresh, nil); act != actionAck {
 		t.Errorf("an ask already answered: action %v, want ack", act)
 	}