diff --git a/lib/Controller/AdminApiController.php b/lib/Controller/AdminApiController.php
index ae1f6a4..37995ec 100644
--- a/lib/Controller/AdminApiController.php
+++ b/lib/Controller/AdminApiController.php
@@ -179,12 +179,12 @@ final class AdminApiController extends Controller {
 		}
 	}
 
-	public function trash(int $targetId, int $offset = 0): JSONResponse {
+	public function trash(int $targetId, string $after = ''): JSONResponse {
 		try {
 			$delay = $this->keys->deleteDelayDays() * 86400;
 			$repo = $this->targets->repository($this->targets->get((string)$targetId));
 			// In parts, so that the page can show how far it is (a read per removed restore point).
-			$page = $repo->trashPage($offset, microtime(true) + self::TRASH_PAGE_SECONDS);
+			$page = $repo->trashPage($after, microtime(true) + self::TRASH_PAGE_SECONDS);
 			$out = [];
 			foreach ($page['items'] as $id => $info) {
 				$out[] = ['id' => $id, 'label' => $info['label'], 'time' => $info['time'], 'removedAt' => $info['forgottenAt'],
diff --git a/lib/Job/BackupRun.php b/lib/Job/BackupRun.php
index 5b42579..4a0c379 100644
--- a/lib/Job/BackupRun.php
+++ b/lib/Job/BackupRun.php
@@ -62,9 +62,9 @@ final class BackupRun {
 				if (!mb_check_encoding($logical, 'UTF-8') || !Repository::isSafePath($logical)) {
 					// A name a snapshot cannot hold (a backslash, a control character, not UTF-8). One
 					// such path must not make a backup fail, or the whole snapshot unreadable later.
+					// The cursor stays where it is: the state is JSON, which cannot hold such a name. A
+					// next step meets it again, and it is reported once.
 					self::recordUnreadable($state, $stats, mb_scrub($logical, 'UTF-8'));
-					$state['cur'] = null;
-					$state['after'] = $logical;
 					continue;
 				}
 				if (is_dir($path)) {
diff --git a/lib/Repository/Repository.php b/lib/Repository/Repository.php
index 398ae20..a631000 100644
--- a/lib/Repository/Repository.php
+++ b/lib/Repository/Repository.php
@@ -818,15 +818,20 @@ final class Repository {
 
 	/**
 	 * Part of trash(), for a page that shows how far it is: each entry is a read of its own on the
-	 * location. Reads on from $offset until $deadline (microtime(true)), at least one entry.
+	 * location. Reads the entries with an id after $after, in order, until $deadline
+	 * (microtime(true)), at least one. The id, not a position: a cleanup that changes the trash
+	 * between two parts then makes no entry come twice or be missed.
 	 *
 	 * @return array{total: int, items: array<string, array<string, mixed>>}
 	 */
-	public function trashPage(int $offset, float $deadline): array {
+	public function trashPage(string $after, float $deadline): array {
 		$ids = array_map('strval', array_keys($this->catalog->trash));
 		sort($ids, SORT_STRING);
 		$items = [];
-		foreach (array_slice($ids, max(0, $offset)) as $id) {
+		foreach ($ids as $id) {
+			if (strcmp($id, $after) <= 0) {
+				continue;
+			}
 			try {
 				$items[$id] = $this->trashInfo($id);
 			} catch (\Throwable) {
diff --git a/src/api.js b/src/api.js
index c5ad161..85b391b 100644
--- a/src/api.js
+++ b/src/api.js
@@ -21,7 +21,7 @@ export default {
 	addSlot: (passphrase, label) => call('post', '/key/slots', { passphrase, label }),
 	replaceSlot: (slot, passphrase, label) => call('put', `/key/slots/${slot}`, { passphrase, label }),
 	removeSlot: (slot) => call('delete', `/key/slots/${slot}`),
-	trash: (targetId, offset = 0) => call('get', `/targets/${targetId}/trash`, { offset }),
+	trash: (targetId, after = '') => call('get', `/targets/${targetId}/trash`, { after }),
 	untrash: (targetId, snapshotId) => call('post', `/targets/${targetId}/trash/${snapshotId}`),
 	kitUrl: () => url('/key/kit'),
 	confirmKit: (accepted, phrase, code) => call('post', '/key/confirm', { accepted, phrase, code }),
diff --git a/src/components/Bin.vue b/src/components/Bin.vue
index 7bdb49b..91d1a40 100644
--- a/src/components/Bin.vue
+++ b/src/components/Bin.vue
@@ -78,13 +78,13 @@ async function loadTarget(target, load) {
 	reading.value = { name: target.name, total: null, done: 0 }
 	const items = []
 	for (;;) {
-		const page = await api.trash(target.id, items.length)
+		const page = await api.trash(target.id, items.length ? items[items.length - 1].id : '')
 		if (load !== current) {
 			return
 		}
 		items.push(...page.items)
 		reading.value = { name: target.name, total: page.total, done: Math.min(items.length, page.total) }
-		if (items.length >= page.total || !page.items.length) {
+		if (!page.items.length || items.length >= page.total) {
 			break
 		}
 	}
diff --git a/tests/Unit/Repository/CatalogTest.php b/tests/Unit/Repository/CatalogTest.php
index bba3047..8bd2646 100644
--- a/tests/Unit/Repository/CatalogTest.php
+++ b/tests/Unit/Repository/CatalogTest.php
@@ -58,16 +58,30 @@ class CatalogTest extends TestCase {
 		$again = $this->open();
 		$seen = [];
 		// A deadline already past: one entry per request, as on a slow location
+		$after = '';
 		for ($request = 0; count($seen) < 3 && $request < 5; $request++) {
-			$page = $again->trashPage(count($seen), 0.0);
+			$page = $again->trashPage($after, 0.0);
 			$this->assertSame(3, $page['total']);
 			$this->assertCount(1, $page['items']);
 			$seen += $page['items'];
+			$after = (string)array_key_last($page['items']);
 		}
-		$this->assertSame(array_keys($again->trash()), array_intersect(array_keys($again->trash()), array_keys($seen)));
-		$this->assertCount(3, $seen);
-		$this->assertSame(['total' => 3, 'items' => []], $again->trashPage(3, 0.0));
-		$this->assertCount(3, $again->trashPage(0, microtime(true) + 60)['items']);
+		$this->assertEqualsCanonicalizing(array_keys($again->trash()), array_keys($seen));
+		$this->assertSame(['total' => 3, 'items' => []], $again->trashPage($after, 0.0));
+		$this->assertCount(3, $again->trashPage('', microtime(true) + 60)['items']);
+	}
+
+	public function testAnEntryThatLeavesTheTrashBetweenPartsMakesNoneComeTwiceOrBeMissed(): void {
+		$repo = Repository::initWithKey($this->backend, $this->keys, $this->keys->wrap('pw'), $this->anchor);
+		for ($i = 0; $i < 3; $i++) {
+			$repo->forget($repo->backupDirectory($this->src)['snapshot']);
+		}
+		$reader = $this->open();
+		$ids = array_keys($reader->trashPage('', microtime(true) + 60)['items']);
+		$first = $reader->trashPage('', 0.0)['items'];
+		$this->assertSame([$ids[0]], array_keys($first));
+		$this->open()->untrash($ids[0]); // another administrator, between two parts
+		$this->assertSame([$ids[1], $ids[2]], array_keys($this->open()->trashPage($ids[0], microtime(true) + 60)['items']));
 	}
 
 	public function testRollbackIsDetected(): void {
diff --git a/tests/Unit/Repository/EmptyDirsTest.php b/tests/Unit/Repository/EmptyDirsTest.php
index b22731e..b318c58 100644
--- a/tests/Unit/Repository/EmptyDirsTest.php
+++ b/tests/Unit/Repository/EmptyDirsTest.php
@@ -78,10 +78,11 @@ class EmptyDirsTest extends TestCase {
 		file_put_contents("$this->src/data/alice/files/\xff.txt", 'x');
 		$state = BackupRun::start(['data' => "$this->src/data"]);
 		for ($i = 0; $i < 50 && $state['phase'] !== 'commit'; $i++) {
-			$state = BackupRun::step($this->repo(), $state, microtime(true) + 30);
+			// A step per entry, state through JSON: as separate processes would
+			$state = json_decode(json_encode(BackupRun::step($this->repo(), $state, 0.0), JSON_THROW_ON_ERROR), true, 512, JSON_THROW_ON_ERROR);
 		}
 		$this->assertSame('commit', $state['phase']);
-		$this->assertSame(4, $state['stats']['unreadable']);
+		$this->assertSame(4, $state['stats']['unreadable'], 'each reported once, over several steps');
 		$this->repo()->recordSnapshot($state['snapshot']);
 
 		$this->assertSame(['data/alice/files/Hollow/Nested', 'data/skipped/inner'], array_column($this->repo()->emptyDirs($state['snapshot']), 0));
diff --git a/tests/integration/roundtrip.sh b/tests/integration/roundtrip.sh
index 0dce2d3..38b0560 100755
--- a/tests/integration/roundtrip.sh
+++ b/tests/integration/roundtrip.sh
@@ -99,7 +99,7 @@ done
 occ backup:list ci | grep " page " >/dev/null || fail "the snapshot of the ticked backup is not listed"
 ok "without system cron: warning in backup:status and the API, backup finished by $i ticks of the open page"
 # The Bin reads in parts, as the page does (what is in the parts: CatalogTest)
-api "$API/targets/$TID/trash?offset=0" | php -r '$p = json_decode(stream_get_contents(STDIN), true); exit(is_int($p["total"] ?? null) && is_array($p["items"] ?? null) && count($p["items"]) <= $p["total"] ? 0 : 1);' || fail "the Bin API does not give a total and items"
+api "$API/targets/$TID/trash" | php -r '$p = json_decode(stream_get_contents(STDIN), true); exit(is_int($p["total"] ?? null) && is_array($p["items"] ?? null) && count($p["items"]) <= $p["total"] ? 0 : 1);' || fail "the Bin API does not give a total and items"
 ok "the Bin API reads in parts, with a total"
 occ background:cron >/dev/null
 $X php -f /var/www/html/cron.php >/dev/null 2>&1 || true