diff --git a/crates/engine/src/tests.rs b/crates/engine/src/tests.rs
index 09d33df8..b2db0a2c 100644
--- a/crates/engine/src/tests.rs
+++ b/crates/engine/src/tests.rs
@@ -380,6 +380,7 @@ fn timeline_edits_reresolve_references() {
     run(&mut s, "UndoCommand", json!({}));
     run(&mut s, "UndoCommand", json!({}));
     assert!(rel(volume(&mut s), 60.0 * 30.0 * 25.0 - f4 - PI * 9.0 * 25.0) < 1e-3);
+}
 
 /// A 40 × 30 × 20 box exported to a STEP file in a fresh temp directory.
 fn step_box_file(tag: &str) -> std::path::PathBuf {
diff --git a/crates/io/src/lib.rs b/crates/io/src/lib.rs
index e92ac7b4..2c13bd9c 100644
--- a/crates/io/src/lib.rs
+++ b/crates/io/src/lib.rs
@@ -61,8 +61,10 @@ pub fn step_import_feature(bytes: &[u8], file: &str) -> Result<StepFeature> {
         .filter(|s| !s.trim().is_empty())
         .unwrap_or_else(|| "Import".into());
     let generic = |n: &str| n.trim().is_empty() || n.starts_with('(') || n.eq_ignore_ascii_case("import") || n.eq_ignore_ascii_case("unnamed");
-    let name = match imp.tree.as_slice() {
-        [root] if !generic(&root.name) => root.name.clone(),
+    // The root product's name; else the only body's name; else the file name.
+    let name = match (imp.tree.as_slice(), imp.bodies.as_slice()) {
+        ([root], _) if !generic(&root.name) => root.name.clone(),
+        (_, [only]) if !generic(&only.name) => only.name.clone(),
         _ => stem,
     };
     let file_name = std::path::Path::new(file).file_name().map(|s| s.to_string_lossy().to_string()).unwrap_or_else(|| file.to_string());
diff --git a/crates/kernel/src/step_in/mod.rs b/crates/kernel/src/step_in/mod.rs
index c6a37272..9dc34846 100644
--- a/crates/kernel/src/step_in/mod.rs
+++ b/crates/kernel/src/step_in/mod.rs
@@ -26,6 +26,9 @@ use p21::{Entity, Exchange, Param};
 const MAX_ASSEMBLY_DEPTH: usize = 32;
 /// Most body instances in one import.
 const MAX_BODIES: usize = 10_000;
+/// Most product occurrences and mapped representations visited (a shared sub-assembly used
+/// twice at every level would otherwise grow exponentially).
+const MAX_VISITS: usize = 100_000;
 
 /// A body read from a STEP file.
 #[derive(Clone, Debug)]
@@ -228,6 +231,8 @@ struct Reader<'a> {
     used_items: HashSet<u64>,
     /// Items already instanced for the product being read.
     node_items: HashSet<u64>,
+    /// Occurrences and mapped representations visited so far.
+    visits: usize,
     bodies: Vec<ImportedBody>,
 }
 
@@ -417,6 +422,11 @@ impl<'a> Reader<'a> {
             self.warn("mapped items nested too deeply");
             return;
         }
+        self.visits += 1;
+        if self.visits > MAX_VISITS {
+            self.warn(format!("more than {MAX_VISITS} component instances: the rest are left out"));
+            return;
+        }
         let u = self.units_of(rep);
         let items = self.reps.get(&rep).map(|r| r.0.clone()).unwrap_or_default();
         for item in items {
@@ -542,6 +552,11 @@ impl<'a> Reader<'a> {
             self.warn("assembly nested too deeply or recursive: some components were left out");
             return node;
         }
+        self.visits += 1;
+        if self.visits > MAX_VISITS {
+            self.warn(format!("more than {MAX_VISITS} component instances: the rest are left out"));
+            return node;
+        }
         stack.push(pd);
         let mut path = path.to_vec();
         path.push(name.clone());
@@ -609,6 +624,7 @@ pub fn step_import(text: &str) -> Result<StepImport> {
         solids: HashMap::new(),
         used_items: HashSet::new(),
         node_items: HashSet::new(),
+        visits: 0,
         bodies: Vec::new(),
     };
     rd.index();
@@ -642,6 +658,7 @@ pub fn step_import(text: &str) -> Result<StepImport> {
     if !loose.is_empty() {
         let mut bodies = Vec::new();
         rd.node_items = rd.used_items.clone();
+        rd.visits = 0;
         for r in loose {
             rd.rep_bodies(r, &identity, &[], "Import", &mut bodies, 0);
         }
diff --git a/crates/kernel/src/step_in/tests.rs b/crates/kernel/src/step_in/tests.rs
index 9387104d..fdf4b739 100644
--- a/crates/kernel/src/step_in/tests.rs
+++ b/crates/kernel/src/step_in/tests.rs
@@ -283,3 +283,26 @@ fn assembly_cycles_are_bounded() {
     let imp = r.unwrap();
     assert_eq!(imp.bodies.len(), 1);
 }
+
+#[test]
+fn exponential_assemblies_are_bounded() {
+    // P0 uses P1 twice, P1 uses P2 twice, … 30 levels: 2^30 occurrences if followed blindly.
+    let mut t = String::from(HEAD);
+    t += "#8=PRODUCT_DEFINITION_CONTEXT('part definition',#9,'design');\n#9=APPLICATION_CONTEXT('');\n";
+    t += &cube_entities();
+    t += &context(20, "(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.))");
+    let levels = 30u64;
+    for l in 0..=levels {
+        t += &product(1000 + l * 10, &format!("P{l}"));
+        if l < levels {
+            for k in 0..2 {
+                t += &format!("#{}=NEXT_ASSEMBLY_USAGE_OCCURRENCE('','','',#{},#{},$);\n", 2000 + l * 10 + k, 1000 + l * 10, 1000 + (l + 1) * 10);
+            }
+        }
+    }
+    t += &format!("#60=ADVANCED_BREP_SHAPE_REPRESENTATION('',(#101),#20);\n#61=SHAPE_DEFINITION_REPRESENTATION(#{},#60);\n", 1000 + levels * 10 + 4);
+    t += TAIL;
+    let imp = step_import(&t).unwrap();
+    assert!(!imp.bodies.is_empty() && imp.bodies.len() <= MAX_BODIES);
+    assert!(imp.warnings.iter().any(|w| w.contains("left out")), "{:?}", imp.warnings);
+}