diff --git a/src/actions.rs b/src/actions.rs
index a703fe36..0102eba4 100644
--- a/src/actions.rs
+++ b/src/actions.rs
@@ -392,10 +392,20 @@ impl EGraph {
                             function.remove(args, self.timestamp);
                         }
                         Change::Subsume => {
-                            if function.decl.merge.is_some() {
+                            if function.decl.subtype != FunctionSubtype::Constructor
+                                && function.decl.subtype != FunctionSubtype::Relation
+                            {
                                 return Err(Error::SubsumeMergeError(*f));
                             }
-                            function.subsume(args);
+                            function
+                                .nodes
+                                .insert_and_merge(args, self.timestamp, true, |old| {
+                                    old.unwrap_or_else(|| Value {
+                                        #[cfg(debug_assertions)]
+                                        tag: function.schema.output.name(),
+                                        bits: self.unionfind.make_set(),
+                                    })
+                                });
                         }
                     }
                     stack.truncate(new_len);
diff --git a/src/function/mod.rs b/src/function/mod.rs
index 22bf4c81..60073598 100644
--- a/src/function/mod.rs
+++ b/src/function/mod.rs
@@ -212,11 +212,6 @@ impl Function {
         res
     }
 
-    /// Mark the given inputs as subsumed.
-    pub fn subsume(&mut self, inputs: &[Value]) {
-        self.nodes.get_mut(inputs).unwrap().subsumed = true;
-    }
-
     /// Return a column index that contains (a superset of) the offsets for the
     /// given column. This method can return nothing if the indexes available
     /// contain too many irrelevant offsets.
diff --git a/src/function/table.rs b/src/function/table.rs
index 78317024..7e59899c 100644
--- a/src/function/table.rs
+++ b/src/function/table.rs
@@ -108,13 +108,6 @@ impl Table {
         Some(&self.vals[off].1)
     }
 
-    pub(crate) fn get_mut(&mut self, inputs: &[Value]) -> Option<&mut TupleOutput> {
-        let hash: u64 = hash_values(inputs);
-        let &TableOffset { off, .. } = self.table.find(hash, self.search_for(hash, inputs))?;
-        debug_assert!(self.vals[off].0.live());
-        Some(&mut self.vals[off].1)
-    }
-
     /// Insert the given data into the table at the given timestamp. Return the
     /// previous value, if there was one.
     pub(crate) fn insert(&mut self, inputs: &[Value], out: Value, ts: u32) -> Option<Value> {
diff --git a/tests/integration_test.rs b/tests/integration_test.rs
index 6e3085d0..0f8d8354 100644
--- a/tests/integration_test.rs
+++ b/tests/integration_test.rs
@@ -350,8 +350,9 @@ fn test_subsume() {
 }
 
 #[test]
-fn test_subsume_primitive() {
-    // Test that we can subsume a primitive
+fn test_subsume_custom() {
+    // Test that we can't subsume  a custom function
+    // Only relations and constructors are allowed to be subsumed
 
     let mut egraph = EGraph::default();
     let res = egraph.parse_and_run_program(
@@ -362,6 +363,29 @@ fn test_subsume_primitive() {
         (subsume (one))
         "#,
     );
+    assert!(res.is_err());
+}
+
+#[test]
+fn test_subsume_ok() {
+    let mut egraph = EGraph::default();
+    let res = egraph.parse_and_run_program(
+        None,
+        r#"
+        (sort E)
+        (constructor one () E)
+        (constructor two () E)
+        (one)
+        (subsume (one))
+        ;; subsuming a non-existent tuple
+        (subsume (two))
+
+        (relation R (i64))
+        (R 1)
+        (subsume (R 1))
+        (subsume (R 2))
+        "#,
+    );
     assert!(res.is_ok());
 }
 
@@ -432,7 +456,7 @@ fn test_serialize_subsume_status() {
         None,
         egglog::SerializedNode::Function {
             name: ("a").into(),
-            offset: 0,
+            offset: 1,
         },
     );
     let b_id = egraph.to_node_id(