diff --git a/crates/circuit/src/dag_circuit.rs b/crates/circuit/src/dag_circuit.rs
index 987d647f20fe..646419601822 100644
--- a/crates/circuit/src/dag_circuit.rs
+++ b/crates/circuit/src/dag_circuit.rs
@@ -1520,7 +1520,14 @@ def _format(operand):
     ///     DAGCircuit: An empty copy of self.
     #[pyo3(signature = (*, vars_mode="alike"))]
     fn copy_empty_like(&self, py: Python, vars_mode: &str) -> PyResult<Self> {
-        let mut target_dag = DAGCircuit::new(py)?;
+        let mut target_dag = DAGCircuit::with_capacity(
+            py,
+            self.num_qubits(),
+            self.num_clbits(),
+            Some(self.num_vars()),
+            None,
+            None,
+        )?;
         target_dag.name = self.name.as_ref().map(|n| n.clone_ref(py));
         target_dag.global_phase = self.global_phase.clone();
         target_dag.duration = self.duration.as_ref().map(|d| d.clone_ref(py));
@@ -6114,31 +6121,41 @@ impl DAGCircuit {
     }
 
     /// Alternative constructor, builds a DAGCircuit with a fixed capacity.
+    /// 
+    /// # Arguments:
+    /// - `py`: Python GIL token
+    /// - `num_qubits`: Number of qubits in the circuit
+    /// - `num_clbits`: Number of classical bits in the circuit.
+    /// - `num_vars`: (Optional) number of variables in the circuit.
+    /// - `num_ops`: (Optional) number of operations in the circuit.
+    /// - `num_edges`: (Optional) If known, number of edges in the circuit.
     pub fn with_capacity(
         py: Python,
         num_qubits: usize,
         num_clbits: usize,
         num_ops: Option<usize>,
         num_vars: Option<usize>,
+        num_edges: Option<usize>,
     ) -> PyResult<Self> {
         let num_ops = num_ops.unwrap_or_default();
         let num_vars = num_vars.unwrap_or_default();
+        let num_edges = num_edges.unwrap_or(
+            num_qubits +    // 1 edge between the input node and the output node or 1st op node.
+            num_clbits +    // 1 edge between the input node and the output node or 1st op node.
+            num_vars +      // 1 edge between the input node and the output node or 1st op node.
+            num_ops, // In Average there will be 3 edges (2 qubits and 1 clbit, or 3 qubits) per op_node.
+        );
 
-        let dag_nodes = num_qubits * 2 + // One input + One output node per qubit
+        let num_nodes = num_qubits * 2 + // One input + One output node per qubit
             num_clbits * 2 +    // One input + One output node per clbit
             num_vars * 2 +  // One input + output node per variable
             num_ops;
 
-        let dag_edges = num_qubits +    // 1 edge between the input node and the output node or 1st op node.
-            num_clbits +    // 1 edge between the input node and the output node or 1st op node.
-            num_vars +      // 1 edge between the input node and the output node or 1st op node.
-            num_ops * 3; // In Average there will be 3 edges (2 qubits and 1 clbit, or 3 qubits) per op_node.
-
         Ok(Self {
             name: None,
             metadata: Some(PyDict::new_bound(py).unbind().into()),
-            calibrations: HashMap::with_capacity(0),
-            dag: StableDiGraph::with_capacity(dag_nodes, dag_edges),
+            calibrations: HashMap::default(),
+            dag: StableDiGraph::with_capacity(num_nodes, num_edges),
             qregs: PyDict::new_bound(py).unbind(),
             cregs: PyDict::new_bound(py).unbind(),
             qargs_cache: IndexedInterner::with_capacity(num_qubits),
@@ -6154,7 +6171,7 @@ impl DAGCircuit {
             clbit_io_map: IndexMap::with_capacity_and_hasher(num_clbits, RandomState::new()),
             var_input_map: _VarIndexMap::new(py),
             var_output_map: _VarIndexMap::new(py),
-            op_names: IndexMap::with_capacity_and_hasher(num_ops, RandomState::new()), // Based on worst case scenario, could be improved
+            op_names: IndexMap::default(),
             control_flow_module: PyControlFlowModule::new(py)?,
             vars_info: HashMap::with_capacity(num_vars),
             vars_by_type: [