diff --git a/crates/doc/src/lib.rs b/crates/doc/src/lib.rs
index 3ae8bbe8..513800e3 100644
--- a/crates/doc/src/lib.rs
+++ b/crates/doc/src/lib.rs
@@ -903,15 +903,22 @@ impl Document {
     /// A unique name like "Frame 3" for a new node of a kind.
     pub fn next_name(&self, base: &str) -> String {
         let mut max = 0u64;
+        let mut taken = std::collections::BTreeSet::new();
         for n in self.nodes() {
             if let Some(rest) = n.name.strip_prefix(base)
                 && let Some(num) = rest.strip_prefix(' ')
                 && let Ok(k) = num.parse::<u64>()
             {
                 max = max.max(k);
+                taken.insert(k);
             }
         }
-        format!("{base} {}", max + 1)
+        let next = match max.checked_add(1) {
+            Some(next) => next,
+            // The counter is spent: the lowest free number instead of wrapping onto a name.
+            None => (1u64..).find(|k| !taken.contains(k)).unwrap_or(1),
+        };
+        format!("{base} {next}")
     }
 
     pub fn style(&self, id: &str) -> Option<&Style> {
diff --git a/crates/doc/src/tests.rs b/crates/doc/src/tests.rs
index ef2f37b9..d54bb29b 100644
--- a/crates/doc/src/tests.rs
+++ b/crates/doc/src/tests.rs
@@ -335,6 +335,16 @@ fn next_name_increments() {
     assert_eq!(d.next_name("Ellipse"), "Ellipse 1");
 }
 
+#[test]
+fn next_name_never_overflows() {
+    let mut d = Document::new("x");
+    let p = page(&d);
+    d.create(p, NodeKind::Frame, "Frame 18446744073709551615", 0.0, 0.0, 1.0, 1.0).unwrap();
+    assert_eq!(d.next_name("Frame"), "Frame 1", "the counter can't step past u64::MAX");
+    d.create(p, NodeKind::Frame, "Frame 1", 0.0, 0.0, 1.0, 1.0).unwrap();
+    assert_eq!(d.next_name("Frame"), "Frame 2");
+}
+
 #[test]
 fn custom_easings() {
     use crate::proto::Easing;
diff --git a/crates/engine/src/cmd/edit.rs b/crates/engine/src/cmd/edit.rs
index 2cfa3a0d..2e4fa2e8 100644
--- a/crates/engine/src/cmd/edit.rs
+++ b/crates/engine/src/cmd/edit.rs
@@ -488,8 +488,9 @@ fn duplicate(s: &mut Session, p: &Value) -> Result<Value> {
 fn bump_name(n: &str) -> String {
     if let Some((base, num)) = n.rsplit_once(' ')
         && let Ok(k) = num.parse::<u64>()
+        && let Some(next) = k.checked_add(1)
     {
-        return format!("{base} {}", k + 1);
+        return format!("{base} {next}");
     }
     format!("{n} 2")
 }
diff --git a/crates/engine/src/panels_behaviour_tests.rs b/crates/engine/src/panels_behaviour_tests.rs
index a5a15a1f..c1016c29 100644
--- a/crates/engine/src/panels_behaviour_tests.rs
+++ b/crates/engine/src/panels_behaviour_tests.rs
@@ -403,3 +403,14 @@ fn assets_panel_lists_files_and_drops_by_the_documented_rules() {
     assert_eq!(kids(&s, row).first(), Some(&into), "an asset dropped in an auto layout frame joins the flow where it is dropped");
     assert_eq!(s.doc().unwrap().page_of(into), Some(page));
 }
+
+#[test]
+fn duplicating_a_layer_named_past_the_counter_does_not_overflow() {
+    let mut s = Session::new();
+    ex(&mut s, "pref.renameDuplicates", json!({"on": true}));
+    let r = rect(&mut s, "r", 30.0, 40.0, None);
+    ex(&mut s, "node.set", json!({"id": r, "props": {"name": "Layer 18446744073709551615"}}));
+    let dup = id_of(&ex(&mut s, "edit.duplicate", json!({"ids": [r]}))["ids"][0]).unwrap();
+    assert_eq!(name(&s, dup), "Layer 18446744073709551615 2");
+    assert!(s.doc().unwrap().validate().is_empty(), "the document still checks out");
+}