diff --git a/crates/engine/src/cmd/fileio/importer.rs b/crates/engine/src/cmd/fileio/importer.rs
index 9fc667c4a..00dfc8d97 100644
--- a/crates/engine/src/cmd/fileio/importer.rs
+++ b/crates/engine/src/cmd/fileio/importer.rs
@@ -58,22 +58,36 @@ pub(super) fn pick(name: &str, bytes: &[u8], p: &Value) -> Result<Option<Arc<Plu
 /// The file at `path` for `document.open`'s params `p`. A file that only an importer reads (one
 /// `importer` names, or an extension no built-in format reads that an importer lists) is read up
 /// to [`import::MAX_INPUT_BYTES`]: past that, it is an error, unless the start of the file shows a
-/// built-in format and no importer was named, which is read whole as any other file is.
+/// built-in format and no importer was named, which is read whole as any other file is. A file past
+/// the limit that isn't read whole is reported from its size, without reading it.
 #[cfg(not(target_arch = "wasm32"))]
 pub(super) fn read_path(path: &str, p: &Value) -> Result<Vec<u8>> {
+    /// How much of the file [`detect`] is given: more than its content checks read.
+    const SNIFF_BYTES: usize = 64 << 10;
+
     let ext = extension(path);
     let explicit = named(p)?.is_some();
     if !explicit && (super::readable_format(&ext).is_some() || import::for_extension(&ext).is_empty()) {
         return super::read_file(path);
     }
-    let head = super::read_file_head(path, import::MAX_INPUT_BYTES + 1)?;
-    if head.len() <= import::MAX_INPUT_BYTES {
+    let head = super::read_file_head(path, SNIFF_BYTES)?;
+    if head.len() < SNIFF_BYTES {
         return Ok(head);
     }
     if !explicit && detect(path, &head).is_some() {
         return super::read_file(path);
     }
-    Err(err(format!("can't open `{}`: {}", file_name(path), import::too_large())))
+    let too_large = || err(format!("can't open `{}`: {}", file_name(path), import::too_large()));
+    let size = std::fs::metadata(path).map_err(|e| EngineError::Other(format!("{path}: {e}")))?.len();
+    if size > import::MAX_INPUT_BYTES as u64 {
+        return Err(too_large());
+    }
+    // The file can grow after the size is read.
+    let file = super::read_file_head(path, import::MAX_INPUT_BYTES + 1)?;
+    if file.len() > import::MAX_INPUT_BYTES {
+        return Err(too_large());
+    }
+    Ok(file)
 }
 
 #[cfg(target_arch = "wasm32")]
diff --git a/crates/engine/src/cmd/fileio/tests.rs b/crates/engine/src/cmd/fileio/tests.rs
index fca92d73f..9755cab52 100644
--- a/crates/engine/src/cmd/fileio/tests.rs
+++ b/crates/engine/src/cmd/fileio/tests.rs
@@ -878,3 +878,26 @@ fn a_photo_places_the_way_its_exif_orientation_says() {
     let red = |p: &image::Rgb<u8>| p[0] > 150 && p[1] < 80;
     assert!(red(px.get_pixel(4, 3)) && !red(px.get_pixel(4, 12)), "the left half is on top");
 }
+
+/// With `importer` named, a file up to the importer's limit is read whole and a larger one is an
+/// error, whatever its content.
+#[test]
+fn read_path_for_a_named_importer_stops_at_the_limit() {
+    let limit = vectorcraft_plugins::import::MAX_INPUT_BYTES as u64;
+    let dir = tmp_dir("read-path-limit");
+    let path = dir.join("drawing.tuv");
+    let name = path.to_string_lossy().into_owned();
+    let named = json!({"importer": "plugin.test.notinstalled"});
+    let sized = |len: u64| {
+        std::fs::write(&path, b"\x89PNG\r\n\x1a\n").unwrap();
+        std::fs::OpenOptions::new().write(true).open(&path).unwrap().set_len(len).unwrap();
+    };
+    for len in [8, 64 << 10, 70_000, limit] {
+        sized(len);
+        assert_eq!(importer::read_path(&name, &named).unwrap().len() as u64, len);
+    }
+    sized(limit + 1);
+    let e = importer::read_path(&name, &named).unwrap_err();
+    assert!(e.to_string().contains("larger than") && e.to_string().contains("drawing.tuv"), "{e}");
+    let _ = std::fs::remove_dir_all(&dir);
+}
diff --git a/crates/engine/tests/plugin_import.rs b/crates/engine/tests/plugin_import.rs
index 7f62de2b7..2abe7f320 100644
--- a/crates/engine/tests/plugin_import.rs
+++ b/crates/engine/tests/plugin_import.rs
@@ -316,3 +316,23 @@ fn a_file_past_the_input_limit_is_refused() {
     assert!(s.documents().is_empty());
     let _ = std::fs::remove_dir_all(&dir);
 }
+
+/// A file past the importer's input limit whose start shows a built-in format opens as that format,
+/// whatever its extension; named, the importer's limit applies to it.
+#[test]
+fn a_built_in_file_past_the_input_limit_still_opens() {
+    let dir = tmp_dir("largebuiltin");
+    let mut s = Session::new();
+    echo(&mut s, "test.largepng", r#"["tsp"]"#);
+    let path = dir.join("big.tsp");
+    let mut png = std::io::Cursor::new(vec![]);
+    image::RgbaImage::new(2, 2).write_to(&mut png, image::ImageFormat::Png).unwrap();
+    std::fs::write(&path, png.get_ref()).unwrap();
+    std::fs::OpenOptions::new().write(true).open(&path).unwrap().set_len(vectorcraft_plugins::import::MAX_INPUT_BYTES as u64 + 1).unwrap();
+    let e = s.execute("document.open", &json!({"path": path_of(&path), "importer": "plugin.test.largepng"})).unwrap_err();
+    assert!(e.to_string().contains("larger than"), "{e}");
+    assert!(s.documents().is_empty());
+    let r = s.execute("document.open", &json!({"path": path_of(&path)})).unwrap();
+    assert_eq!(r["format"], "png");
+    let _ = std::fs::remove_dir_all(&dir);
+}