diff --git a/docs/reference/sparql-anything.md b/docs/reference/sparql-anything.md
index ef915e4e..65510270 100644
--- a/docs/reference/sparql-anything.md
+++ b/docs/reference/sparql-anything.md
@@ -144,7 +144,7 @@ Set `extension` for a tool that reads the format from the file name – SPARQL A
 
 **Splitting is by line**, so every record must be one line. A delimited format that wraps a field in quotes to carry a newline inside it would be cut in two; tab-separated exports, N-Triples and NDJSON are one record per line by definition. Line endings are normalised to `\n`.
 
-Chunks of the same input left by an earlier call are removed first, so a re-run cannot leave a longer run's tail behind for something to pick up. Only those: everything else in the directory is the caller's.
+Chunks of the same input left by an earlier call are removed first, so a re-run cannot leave a longer run's tail behind for something to pick up. Only those: everything else in the directory is the caller's. Take the paths `chunk()` returns as the list of chunks to convert, rather than rediscovering them by name in the directory – a listing would also pick up whatever else is there.
 
 An input with no rows is an error rather than an empty set of chunks: a step that produced an empty file has already failed.
 
diff --git a/packages/sparql-anything/src/chunk.ts b/packages/sparql-anything/src/chunk.ts
index cc10435f..85715535 100644
--- a/packages/sparql-anything/src/chunk.ts
+++ b/packages/sparql-anything/src/chunk.ts
@@ -146,8 +146,10 @@ async function removeChunksOf(
   extension: string,
   into: string,
 ): Promise<void> {
+  // Four digits or more: the index is padded to four, and grows past them
+  // from the 10,000th chunk on.
   const chunkFile = new RegExp(
-    `^${escapeForRegExp(name)}-\\d{4}${escapeForRegExp(extension)}$`,
+    `^${escapeForRegExp(name)}-\\d{4,}${escapeForRegExp(extension)}$`,
   );
   const entries = await readdir(into, { withFileTypes: true });
   await Promise.all(
diff --git a/packages/sparql-anything/test/chunk.test.ts b/packages/sparql-anything/test/chunk.test.ts
index ddce13c9..dccff599 100644
--- a/packages/sparql-anything/test/chunk.test.ts
+++ b/packages/sparql-anything/test/chunk.test.ts
@@ -183,6 +183,29 @@ describe('chunk', () => {
     ]);
   });
 
+  // Writing 10,001 files takes a few seconds, so leave it room on a slow runner.
+  it(
+    'removes chunks past the 10,000th, whose index has five digits',
+    { timeout: 30_000 },
+    async () => {
+      const into = join(workDir, 'chunks');
+      const input = join(workDir, 'places.txt');
+      // One character per row keeps 10,001 rows small.
+      await writeFile(input, 'x\n'.repeat(10_001));
+      const firstPaths = await chunk(input, { rows: 1, into });
+      expect(firstPaths[10_000].endsWith('places-10000.txt')).toBe(true);
+
+      const secondPaths = await chunk(input, { rows: 5_000, into });
+
+      expect(secondPaths).toHaveLength(3);
+      expect((await readdir(into)).sort()).toEqual([
+        'places-0000.txt',
+        'places-0001.txt',
+        'places-0002.txt',
+      ]);
+    },
+  );
+
   it('refuses an extension without its leading dot', async () => {
     const input = await writeInput(2);