diff --git a/internal/imap/imap.go b/internal/imap/imap.go
index fa27d22..cd1465e 100644
--- a/internal/imap/imap.go
+++ b/internal/imap/imap.go
@@ -135,6 +135,21 @@ func (c *Client) Since(uid uint32, limit int) ([]Message, uint32, error) {
 	}
 
 	uids := found.AllUIDs()
+
+	// Anything at or below the marker is dropped here rather than trusted to the
+	// range in the query. A server that reads `1272:*` as `0:1272` — and one does,
+	// which is how the same mail became a task every ten minutes with the marker
+	// standing still at 1271 — hands back the whole mailbox. The marker is ours;
+	// enforcing it here costs one pass over a list of at most a few hundred
+	// numbers and does not depend on anybody else's reading of the spec.
+	kept := make([]imap.UID, 0, len(uids))
+	for _, u := range uids {
+		if uint32(u) > uid {
+			kept = append(kept, u)
+		}
+	}
+	uids = kept
+
 	if len(uids) == 0 {
 		return nil, uid, nil
 	}
diff --git a/internal/imap/roundtrip_test.go b/internal/imap/roundtrip_test.go
index d96046a..5eebe48 100644
--- a/internal/imap/roundtrip_test.go
+++ b/internal/imap/roundtrip_test.go
@@ -262,3 +262,57 @@ func TestAMultipartMailReadsAsItsText(t *testing.T) {
 		t.Errorf("the snippet does not start with the text of the mail: %q", got)
 	}
 }
+
+// The marker is ours, not the server's.
+//
+// A mailbox read with a marker above everything in it must come back empty. The
+// query says so, but a server is free to read the range differently — one reads
+// `1272:*` as `0:1272` and hands back the lot, which is how the same mail became
+// a task every ten minutes while the marker stood still at 1271. The filter is
+// on this side now, so the invariant holds whatever comes back.
+func TestNothingAtOrBelowTheMarkerComesBack(t *testing.T) {
+	addr, pool := serveMailbox(t, []mail{
+		{subject: "En", from: "a@example.dk", body: "en", flagged: true},
+		{subject: "To", from: "b@example.dk", body: "to", flagged: true},
+		{subject: "Tre", from: "c@example.dk", body: "tre", flagged: true},
+	})
+	client, err := Dial(Account{Host: addr, Username: "kw", Password: "hemmelig", RootCAs: pool})
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer client.Close()
+
+	all, highest, err := client.Since(0, 25)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if len(all) != 3 {
+		t.Fatalf("got %d messages on the first read, want 3", len(all))
+	}
+
+	// Read again from the marker the first run would have written.
+	rest, again, err := client.Since(highest, 25)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if len(rest) != 0 {
+		t.Errorf("%d message(s) came back at or below the marker: %v", len(rest), rest[0].Subject)
+	}
+	// And the marker must not go backwards, or the next run reads them all again.
+	if again < highest {
+		t.Errorf("the marker moved back from %d to %d", highest, again)
+	}
+
+	// Every message, individually: none of them may reappear once passed.
+	for _, m := range all {
+		later, _, err := client.Since(m.UID, 25)
+		if err != nil {
+			t.Fatal(err)
+		}
+		for _, l := range later {
+			if l.UID <= m.UID {
+				t.Errorf("reading from %d gave %d back", m.UID, l.UID)
+			}
+		}
+	}
+}
diff --git a/internal/store/savemailbox_test.go b/internal/store/savemailbox_test.go
new file mode 100644
index 0000000..2447f8d
--- /dev/null
+++ b/internal/store/savemailbox_test.go
@@ -0,0 +1,40 @@
+package store
+
+import (
+	"context"
+	"testing"
+)
+
+// Saving a mailbox that is already there must update it, not fail.
+//
+// The row is written again on every token refresh and every time Gmail's seen
+// list changes. If that write errors, the tasks a sync made are kept and the note
+// of having made them is not — so the same mail becomes a task again on the next
+// sweep, once every ten minutes, forever.
+func TestSavingAnExistingMailboxUpdatesIt(t *testing.T) {
+	db, userID := sealedStore(t)
+	ctx := context.Background()
+
+	m := &Mailbox{UserID: userID, Kind: "gmail", Username: "kw@nolimit.dk",
+		RefreshToken: "r", Seen: []string{"a"}}
+	if err := db.SaveMailbox(ctx, m); err != nil {
+		t.Fatal(err)
+	}
+
+	m.Seen = []string{"a", "b"}
+	m.AccessToken = "fresh"
+	if err := db.SaveMailbox(ctx, m); err != nil {
+		t.Fatalf("saving it a second time failed: %v", err)
+	}
+
+	back, err := db.MailboxOfKind(ctx, userID, "gmail")
+	if err != nil {
+		t.Fatal(err)
+	}
+	if len(back.Seen) != 2 {
+		t.Errorf("the seen list came back as %v", back.Seen)
+	}
+	if back.AccessToken != "fresh" {
+		t.Errorf("the token came back as %q", back.AccessToken)
+	}
+}