diff --git a/src/circuit.rs b/src/circuit.rs
index 8f9e9a22..5bf0d1ff 100644
--- a/src/circuit.rs
+++ b/src/circuit.rs
@@ -9,10 +9,18 @@ pub use hash::CircuitHash;
 
 use hugr::HugrView;
 
+use derive_more::From;
+use hugr::hugr::hugrmut::HugrMut;
+use hugr::hugr::{NodeType, PortIndex};
+use hugr::ops::dataflow::IOTrait;
 pub use hugr::ops::OpType;
+use hugr::ops::{Input, Output, DFG};
 use hugr::types::FunctionType;
 pub use hugr::types::{EdgeKind, Signature, Type, TypeRow};
 pub use hugr::{Node, Port, Wire};
+use itertools::Itertools;
+use portgraph::Direction;
+use thiserror::Error;
 
 use self::units::{filter, FilteredUnits, Units};
 
@@ -120,18 +128,164 @@ pub trait Circuit: HugrView {
     }
 }
 
+/// Remove an empty wire in a dataflow HUGR.
+///
+/// The wire to be removed is identified by the index of the outgoing port
+/// at the circuit input node.
+///
+/// This will change the circuit signature and will shift all ports after
+/// the removed wire by -1. If the wire is connected to the output node,
+/// this will also change the signature output and shift the ports after
+/// the removed wire by -1.
+///
+/// This will return an error if the wire is not empty or if a HugrError
+/// occurs.
+#[allow(dead_code)]
+pub(crate) fn remove_empty_wire(
+    circ: &mut impl HugrMut,
+    input_port: usize,
+) -> Result<(), CircuitMutError> {
+    let [inp, out] = circ.get_io(circ.root()).expect("no IO nodes found at root");
+    if input_port >= circ.num_outputs(inp) {
+        return Err(CircuitMutError::InvalidPortOffset(input_port));
+    }
+    let input_port = Port::new_outgoing(input_port);
+    let link = circ
+        .linked_ports(inp, input_port)
+        .at_most_one()
+        .map_err(|_| CircuitMutError::DeleteNonEmptyWire(input_port.index()))?;
+    if link.is_some() && link.unwrap().0 != out {
+        return Err(CircuitMutError::DeleteNonEmptyWire(input_port.index()));
+    }
+    if link.is_some() {
+        circ.disconnect(inp, input_port)?;
+    }
+
+    // Shift ports at input
+    shift_ports(circ, inp, input_port, circ.num_outputs(inp))?;
+    // Shift ports at output
+    if let Some((out, output_port)) = link {
+        shift_ports(circ, out, output_port, circ.num_inputs(out))?;
+    }
+    // Update input node, output node (if necessary) and root signatures.
+    update_signature(circ, input_port.index(), link.map(|(_, p)| p.index()));
+    // Resize ports at input/output node
+    circ.set_num_ports(inp, 0, circ.num_outputs(inp) - 1);
+    if let Some((out, _)) = link {
+        circ.set_num_ports(out, circ.num_inputs(out) - 1, 0);
+    }
+    Ok(())
+}
+
+/// Errors that can occur when mutating a circuit.
+#[derive(Debug, Clone, Error, PartialEq, Eq, From)]
+pub enum CircuitMutError {
+    /// A Hugr error occurred.
+    #[error("Hugr error: {0:?}")]
+    HugrError(hugr::hugr::HugrError),
+    /// The wire to be deleted is not empty.
+    #[from(ignore)]
+    #[error("Wire {0} cannot be deleted: not empty")]
+    DeleteNonEmptyWire(usize),
+    /// The wire does not exist.
+    #[from(ignore)]
+    #[error("Wire {0} does not exist")]
+    InvalidPortOffset(usize),
+}
+
+/// Shift ports in range (free_port + 1 .. max_ind) by -1.
+fn shift_ports<C: HugrMut + ?Sized>(
+    circ: &mut C,
+    node: Node,
+    mut free_port: Port,
+    max_ind: usize,
+) -> Result<Port, hugr::hugr::HugrError> {
+    let dir = free_port.direction();
+    let port_range = (free_port.index() + 1..max_ind).map(|p| Port::new(dir, p));
+    for port in port_range {
+        let links = circ.linked_ports(node, port).collect_vec();
+        if !links.is_empty() {
+            circ.disconnect(node, port)?;
+        }
+        for (other_n, other_p) in links {
+            // TODO: simplify when CQCL-DEV/hugr#565 is resolved
+            match dir {
+                Direction::Incoming => circ.connect(other_n, other_p, node, free_port),
+                Direction::Outgoing => circ.connect(node, free_port, other_n, other_p),
+            }?;
+        }
+        free_port = port;
+    }
+    Ok(free_port)
+}
+
+// Update the signature of circ when removing the in_index-th input wire and
+// the out_index-th output wire.
+fn update_signature<C: HugrMut + Circuit + ?Sized>(
+    circ: &mut C,
+    in_index: usize,
+    out_index: Option<usize>,
+) {
+    let inp = circ.input();
+    // Update input node
+    let inp_types: TypeRow = {
+        let OpType::Input(Input { types }) = circ.get_optype(inp).clone() else {
+            panic!("invalid circuit")
+        };
+        let mut types = types.into_owned();
+        types.remove(in_index);
+        types.into()
+    };
+    let new_inp_op = Input::new(inp_types.clone());
+    let inp_exts = circ.get_nodetype(inp).input_extensions().cloned();
+    circ.replace_op(inp, NodeType::new(new_inp_op, inp_exts));
+
+    // Update output node if necessary.
+    let out_types = out_index.map(|out_index| {
+        let out = circ.output();
+        let out_types: TypeRow = {
+            let OpType::Output(Output { types }) = circ.get_optype(out).clone() else {
+                panic!("invalid circuit")
+            };
+            let mut types = types.into_owned();
+            types.remove(out_index);
+            types.into()
+        };
+        let new_out_op = Output::new(out_types.clone());
+        let inp_exts = circ.get_nodetype(out).input_extensions().cloned();
+        circ.replace_op(out, NodeType::new(new_out_op, inp_exts));
+        out_types
+    });
+
+    // Update root
+    let OpType::DFG(DFG { mut signature, .. }) = circ.get_optype(circ.root()).clone() else {
+        panic!("invalid circuit")
+    };
+    signature.input = inp_types;
+    if let Some(out_types) = out_types {
+        signature.output = out_types;
+    }
+    let new_dfg_op = DFG { signature };
+    let inp_exts = circ.get_nodetype(circ.root()).input_extensions().cloned();
+    circ.replace_op(circ.root(), NodeType::new(new_dfg_op, inp_exts));
+}
+
 impl<T> Circuit for T where T: HugrView {}
 
 #[cfg(test)]
 mod tests {
-    use hugr::Hugr;
+    use hugr::{
+        builder::{DFGBuilder, DataflowHugr},
+        extension::{prelude::BOOL_T, PRELUDE_REGISTRY},
+        Hugr,
+    };
 
-    use crate::{circuit::Circuit, json::load_tk1_json_str};
+    use super::*;
+    use crate::{json::load_tk1_json_str, utils::build_simple_circuit, T2Op};
 
     fn test_circuit() -> Hugr {
         load_tk1_json_str(
-            r#"{
-            "phase": "0",
+            r#"{ "phase": "0",
             "bits": [["c", [0]]],
             "qubits": [["q", [0]], ["q", [1]]],
             "commands": [
@@ -160,4 +314,35 @@ mod tests {
         assert_eq!(circ.linear_units().count(), 3);
         assert_eq!(circ.qubits().count(), 2);
     }
+
+    #[test]
+    fn remove_qubit() {
+        let mut circ = build_simple_circuit(2, |circ| {
+            circ.append(T2Op::X, [0])?;
+            Ok(())
+        })
+        .unwrap();
+
+        assert_eq!(circ.qubit_count(), 2);
+        assert!(remove_empty_wire(&mut circ, 1).is_ok());
+        assert_eq!(circ.qubit_count(), 1);
+        assert_eq!(
+            remove_empty_wire(&mut circ, 0).unwrap_err(),
+            CircuitMutError::DeleteNonEmptyWire(0)
+        );
+    }
+
+    #[test]
+    fn remove_bit() {
+        let h = DFGBuilder::new(FunctionType::new(vec![BOOL_T], vec![])).unwrap();
+        let mut circ = h.finish_hugr_with_outputs([], &PRELUDE_REGISTRY).unwrap();
+
+        assert_eq!(circ.units().count(), 1);
+        assert!(remove_empty_wire(&mut circ, 0).is_ok());
+        assert_eq!(circ.units().count(), 0);
+        assert_eq!(
+            remove_empty_wire(&mut circ, 2).unwrap_err(),
+            CircuitMutError::InvalidPortOffset(2)
+        );
+    }
 }