diff --git a/crates/project/src/comp.rs b/crates/project/src/comp.rs
index aa4ff7201..3bce67960 100644
--- a/crates/project/src/comp.rs
+++ b/crates/project/src/comp.rs
@@ -271,7 +271,15 @@ impl Comp {
             return base.to_string();
         }
         let stem = base.trim_end_matches(|c: char| c.is_ascii_digit()).trim_end();
-        (2..).map(|i| format!("{stem} {i}")).find(|n| !self.layers.iter().any(|l| &l.name == n)).unwrap_or_default()
+        // The suffixes in use, gathered in one pass: trying each candidate against every layer
+        // made importing many layers of one name cubic.
+        let taken: std::collections::HashSet<u64> = self
+            .layers
+            .iter()
+            .filter_map(|l| l.name.strip_prefix(stem)?.strip_prefix(' '))
+            .filter_map(|s| s.parse::<u64>().ok().filter(|n| n.to_string() == s))
+            .collect();
+        (2..).find(|i| !taken.contains(i)).map(|i| format!("{stem} {i}")).unwrap_or_default()
     }
 }
 
diff --git a/crates/project/src/render_queue.rs b/crates/project/src/render_queue.rs
index c40096905..f7759cff4 100644
--- a/crates/project/src/render_queue.rs
+++ b/crates/project/src/render_queue.rs
@@ -1529,7 +1529,11 @@ pub fn numbered_template(template: &str, n: u32) -> String {
 
 /// Make a name safe as a file name component.
 pub fn sanitize(name: &str) -> String {
-    name.chars().map(|c| if matches!(c, '/' | '\\' | ':' | '*' | '?' | '"' | '<' | '>' | '|') { '_' } else { c }).collect()
+    // At most a file name's worth (255 characters): a template repeating a long name token
+    // must not expand to gigabytes.
+    let s: String = name.chars().take(255).map(|c| if matches!(c, '/' | '\\' | ':' | '*' | '?' | '"' | '<' | '>' | '|') { '_' } else { c }).collect();
+    // `.` and `..` would name the folder itself or its parent when the token is a path component.
+    if !s.is_empty() && s.chars().all(|c| c == '.') { "_".repeat(s.len()) } else { s }
 }
 
 #[cfg(test)]
@@ -1540,6 +1544,14 @@ mod tests {
     fn templates_and_sequences() {
         let v = TemplateVars { comp_name: "Main/Title", project_name: "P", width: 1920, height: 1080, frame_rate: 29.97, start_frame: 0, end_frame: 9 };
         assert_eq!(expand_template(DEFAULT_TEMPLATE, OutputFormat::H264, &v), "Main_Title.mp4");
+        // A dot-only name is not a parent-folder component; a long one is cut to a file name.
+        for name in ["..", "."] {
+            let v = TemplateVars { comp_name: name, ..v };
+            assert_eq!(expand_template("out/[compName]/x.[fileExtension]", OutputFormat::Gif, &v), format!("out/{}/x.gif", "_".repeat(name.len())));
+        }
+        let long = "n".repeat(100_000);
+        let v2 = TemplateVars { comp_name: &long, ..v };
+        assert_eq!(expand_template(&"[compName]".repeat(100), OutputFormat::Gif, &v2).len(), 255 * 100);
         assert_eq!(expand_template("[compName]_[width]x[height]@[frameRate].[fileExtension]", OutputFormat::Gif, &v), "Main_Title_1920x1080@29.97.gif");
         assert_eq!(sequence_path("out/a_[#####].png", 42), "out/a_00042.png");
         assert_eq!(sequence_path("a###.tif", 7), "a007.tif");
diff --git a/crates/project/src/tests.rs b/crates/project/src/tests.rs
index a47792b89..a5f0bbab1 100644
--- a/crates/project/src/tests.rs
+++ b/crates/project/src/tests.rs
@@ -119,6 +119,14 @@ fn unique_names_and_cycles() {
     let c = p.comp(cid).unwrap();
     assert_eq!(c.unique_layer_name("Red Solid 1"), "Red Solid 2");
     assert_eq!(c.unique_layer_name("Shape Layer 1"), "Shape Layer 1");
+    // A suffix written another way (`02`) is not the number taken.
+    let mut d = c.clone();
+    for n in ["Red Solid 02", "Red Solid 3"] {
+        let mut l = d.layers[0].clone();
+        l.name = n.into();
+        d.layers.push(l);
+    }
+    assert_eq!(d.unique_layer_name("Red Solid 1"), "Red Solid 2");
     assert!(p.comp_contains(cid, cid));
 }