diff --git a/hugr-passes/Cargo.toml b/hugr-passes/Cargo.toml
index 467c92505..161566cfc 100644
--- a/hugr-passes/Cargo.toml
+++ b/hugr-passes/Cargo.toml
@@ -18,6 +18,7 @@ itertools = { workspace = true }
 lazy_static = { workspace = true }
 paste = { workspace = true }
 thiserror = { workspace = true }
+petgraph = { workspace = true }
 
 [features]
 extension_inference = ["hugr-core/extension_inference"]
diff --git a/hugr-passes/src/force_order.rs b/hugr-passes/src/force_order.rs
new file mode 100644
index 000000000..4278b2879
--- /dev/null
+++ b/hugr-passes/src/force_order.rs
@@ -0,0 +1,307 @@
+//! Provides [force_order], a tool for fixing the order of nodes in a Hugr.
+use std::{cmp::Reverse, collections::BinaryHeap};
+
+use hugr_core::{
+    hugr::{
+        hugrmut::HugrMut,
+        views::{DescendantsGraph, HierarchyView, SiblingGraph},
+        HugrError,
+    },
+    ops::{OpTag, OpTrait},
+    types::EdgeKind,
+    Direction, HugrView as _, Node,
+};
+use itertools::Itertools as _;
+use petgraph::{
+    visit::{
+        GraphBase, GraphRef, IntoNeighbors as _, IntoNeighborsDirected, IntoNodeIdentifiers,
+        NodeFiltered, VisitMap, Visitable, Walker,
+    },
+    Direction::Incoming,
+};
+
+/// Insert order edges into a Hugr according to a rank function.
+///
+/// All dataflow parents which are transitive children of `root`, including
+/// `root` itself, will have their dataflow regions ordered.
+///
+/// Dataflow regions are ordered by inserting order edges between their
+/// immediate children. A dataflow parent with `C` children will have at most
+/// `C-1` edges added. Any node than can be ordered will be.
+///
+/// Nodes are ordered according to the `rank` function. Nodes of lower rank will
+/// be ordered earlier in their parent. Note that if  `rank(n1) < rank(n2)` it
+/// is not guaranteed that `n1` will be ordered before `n2`. If `n1` dominates
+/// `n2` it cannot be ordered after `n1` without invalidating `hugr`.  Nodes of
+/// equal rank will be ordered arbitrarily, although that arbitrary order is
+/// deterministic.
+pub fn force_order(
+    hugr: &mut impl HugrMut,
+    root: Node,
+    rank: impl Fn(Node) -> i64,
+) -> Result<(), HugrError> {
+    force_order_by_key(hugr, root, rank)
+}
+
+/// As [force_order], but allows a generic [Ord] choice for the result of the
+/// `rank` function.
+pub fn force_order_by_key<K: Ord>(
+    hugr: &mut impl HugrMut,
+    root: Node,
+    rank: impl Fn(Node) -> K,
+) -> Result<(), HugrError> {
+    let dataflow_parents = DescendantsGraph::<Node>::try_new(hugr, root)?
+        .nodes()
+        .filter(|n| hugr.get_optype(*n).tag() <= OpTag::DataflowParent)
+        .collect_vec();
+    for dp in dataflow_parents {
+        let sg = SiblingGraph::<Node>::try_new(hugr, dp)?;
+        let petgraph = NodeFiltered::from_fn(sg.as_petgraph(), |x| x != dp);
+        let ordered_nodes = ForceOrder::new(&petgraph, &rank)
+            .iter(&petgraph)
+            .filter(|&x| hugr.get_optype(x).tag() <= OpTag::DataflowChild)
+            .collect_vec();
+
+        for (&n1, &n2) in ordered_nodes.iter().tuple_windows() {
+            let (n1_ot, n2_ot) = (hugr.get_optype(n1), hugr.get_optype(n2));
+            assert_eq!(
+                Some(EdgeKind::StateOrder),
+                n1_ot.other_port_kind(Direction::Outgoing),
+                "Node {n1} does not support state order edges"
+            );
+            assert_eq!(
+                Some(EdgeKind::StateOrder),
+                n2_ot.other_port_kind(Direction::Incoming),
+                "Node {n2} does not support state order edges"
+            );
+            if !hugr.output_neighbours(n1).contains(&n2) {
+                hugr.connect(
+                    n1,
+                    n1_ot.other_output_port().unwrap(),
+                    n2,
+                    n2_ot.other_input_port().unwrap(),
+                );
+            }
+        }
+    }
+
+    Ok(())
+}
+
+/// An adaption of [petgraph::visit::Topo]. We differ only in that we sort nodes
+/// by the rank function before adding them to the internal work stack. This
+/// ensures we visit lower ranked nodes before higher ranked nodes whenever the
+/// topology of the graph allows.
+#[derive(Clone)]
+struct ForceOrder<K, N, VM, F> {
+    tovisit: BinaryHeap<(Reverse<K>, N)>,
+    ordered: VM,
+    rank: F,
+}
+
+impl<K: Ord, N: Ord, VM, F: Fn(N) -> K> ForceOrder<K, N, VM, F>
+where
+    N: Copy + PartialEq,
+    VM: VisitMap<N>,
+{
+    pub fn new<G>(graph: G, rank: F) -> Self
+    where
+        G: IntoNodeIdentifiers + IntoNeighborsDirected + Visitable<NodeId = N, Map = VM>,
+    {
+        let mut topo = Self::empty(graph, rank);
+        topo.extend_with_initials(graph);
+        topo
+    }
+
+    fn empty<G>(graph: G, rank: F) -> Self
+    where
+        G: GraphRef + Visitable<NodeId = N, Map = VM>,
+    {
+        Self {
+            ordered: graph.visit_map(),
+            tovisit: Default::default(),
+            rank,
+        }
+    }
+
+    fn extend_with_initials<G>(&mut self, g: G)
+    where
+        G: IntoNodeIdentifiers + IntoNeighborsDirected<NodeId = N>,
+    {
+        // find all initial nodes (nodes without incoming edges)
+        self.extend(
+            g.node_identifiers()
+                .filter(move |&a| g.neighbors_directed(a, Incoming).next().is_none()),
+        );
+    }
+
+    fn extend(&mut self, new_nodes: impl IntoIterator<Item = N>) {
+        self.tovisit
+            .extend(new_nodes.into_iter().map(|x| (Reverse((self.rank)(x)), x)));
+    }
+
+    /// Return the next node in the current topological order traversal, or
+    /// `None` if the traversal is at the end.
+    ///
+    /// *Note:* The graph may not have a complete topological order, and the only
+    /// way to know is to run the whole traversal and make sure it visits every node.
+    pub fn next<G>(&mut self, g: G) -> Option<N>
+    where
+        G: IntoNeighborsDirected + Visitable<NodeId = N, Map = VM>,
+    {
+        // Take an unvisited element and find which of its neighbors are next
+        while let Some((_, nix)) = self.tovisit.pop() {
+            if self.ordered.is_visited(&nix) {
+                continue;
+            }
+            self.ordered.visit(nix);
+            // Look at each neighbor, and those that only have incoming edges
+            // from the already ordered list, they are the next to visit.
+            let new_nodes = g
+                .neighbors(nix)
+                .filter(|&n| {
+                    petgraph::visit::Reversed(g)
+                        .neighbors(n)
+                        .all(|b| self.ordered.is_visited(&b))
+                })
+                .collect_vec();
+
+            self.extend(new_nodes);
+            return Some(nix);
+        }
+        None
+    }
+}
+
+impl<K: Ord, G: Visitable + IntoNeighborsDirected, F: Fn(G::NodeId) -> K> Walker<G>
+    for ForceOrder<K, G::NodeId, G::Map, F>
+where
+    G::NodeId: Ord,
+{
+    type Item = <G as GraphBase>::NodeId;
+
+    fn walk_next(&mut self, g: G) -> Option<Self::Item> {
+        self.next(g)
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use std::collections::HashMap;
+
+    use super::*;
+    use hugr_core::builder::{BuildHandle, Dataflow, DataflowHugr};
+    use hugr_core::ops::handle::{DataflowOpID, NodeHandle};
+
+    use hugr_core::std_extensions::arithmetic::int_ops::{self, IntOpDef};
+    use hugr_core::std_extensions::arithmetic::int_types::INT_TYPES;
+    use hugr_core::types::FunctionType;
+    use hugr_core::{builder::DFGBuilder, hugr::Hugr};
+    use hugr_core::{HugrView, Wire};
+
+    use petgraph::visit::Topo;
+
+    const I: u8 = 3;
+
+    fn build_neg(builder: &mut impl Dataflow, wire: Wire) -> BuildHandle<DataflowOpID> {
+        builder
+            .add_dataflow_op(IntOpDef::ineg.with_log_width(I), [wire])
+            .unwrap()
+    }
+
+    fn build_add(builder: &mut impl Dataflow, w1: Wire, w2: Wire) -> BuildHandle<DataflowOpID> {
+        builder
+            .add_dataflow_op(IntOpDef::iadd.with_log_width(I), [w1, w2])
+            .unwrap()
+    }
+
+    /// Our tests use the following hugr:
+    ///
+    /// a DFG with sig: [i8,i8] -> [i8,i8]
+    ///
+    ///         Input
+    ///    |        |
+    ///    | iw1    | iw2
+    ///   v0(neg)  v1(neg)
+    ///    |   \    |
+    ///    |    \   |
+    ///    |     \  |
+    ///   v2(neg)  v3(add)
+    ///    |        |
+    ///      Output
+    fn test_hugr() -> (Hugr, [Node; 4]) {
+        let t = INT_TYPES[I as usize].clone();
+        let mut builder =
+            DFGBuilder::new(FunctionType::new_endo(vec![t.clone(), t.clone()])).unwrap();
+        let [iw1, iw2] = builder.input_wires_arr();
+        let v0 = build_neg(&mut builder, iw1);
+        let v1 = build_neg(&mut builder, iw2);
+        let v2 = build_neg(&mut builder, v0.out_wire(0));
+        let v3 = build_add(&mut builder, v0.out_wire(0), v1.out_wire(0));
+        let nodes = [v0, v1, v2, v3]
+            .into_iter()
+            .map(|x| x.handle().node())
+            .collect_vec()
+            .try_into()
+            .unwrap();
+        (
+            builder
+                .finish_hugr_with_outputs(
+                    [v2.out_wire(0), v3.out_wire(0)],
+                    &int_ops::INT_OPS_REGISTRY,
+                )
+                .unwrap(),
+            nodes,
+        )
+    }
+
+    type RankMap = HashMap<Node, i64>;
+
+    fn force_order_test_impl(hugr: &mut Hugr, rank_map: RankMap) -> Vec<Node> {
+        force_order(hugr, hugr.root(), |n| *rank_map.get(&n).unwrap_or(&0)).unwrap();
+
+        let topo_sorted = Topo::new(&hugr.as_petgraph())
+            .iter(&hugr.as_petgraph())
+            .filter(|n| rank_map.contains_key(n))
+            .collect_vec();
+        hugr.validate_no_extensions(&int_ops::INT_OPS_REGISTRY)
+            .unwrap();
+
+        topo_sorted
+    }
+
+    #[test]
+    fn test_force_order_1() {
+        let (mut hugr, [v0, v1, v2, v3]) = test_hugr();
+
+        // v0 has a higher rank than v2, but v0 dominates v2, so cannot be
+        // ordered before it.
+        //
+        // v1 and v3 are pushed to the bottom of the graph with high weights.
+        let rank_map = [(v0, 2), (v2, 1), (v1, 10), (v3, 9)].into_iter().collect();
+
+        let topo_sort = force_order_test_impl(&mut hugr, rank_map);
+        assert_eq!(vec![v0, v2, v1, v3], topo_sort);
+    }
+
+    #[test]
+    fn test_force_order_2() {
+        let (mut hugr, [v0, v1, v2, v3]) = test_hugr();
+
+        // v1 and v3 are pulled to the top of the graph with low weights.
+        // v3 cannot ascend past v0 because it is dominated by v0
+        let rank_map = [(v0, 2), (v2, 1), (v1, -10), (v3, -9)]
+            .into_iter()
+            .collect();
+        let topo_sort = force_order_test_impl(&mut hugr, rank_map);
+        assert_eq!(vec![v1, v0, v3, v2], topo_sort);
+    }
+
+    #[test]
+    fn test_force_order_3() {
+        let (mut hugr, [v0, v1, v2, v3]) = test_hugr();
+        let rank_map = [(v0, 0), (v1, 1), (v2, 2), (v3, 3)].into_iter().collect();
+        let topo_sort = force_order_test_impl(&mut hugr, rank_map);
+        assert_eq!(vec![v0, v1, v2, v3], topo_sort);
+    }
+}
diff --git a/hugr-passes/src/lib.rs b/hugr-passes/src/lib.rs
index f6e09b71b..f477d27cb 100644
--- a/hugr-passes/src/lib.rs
+++ b/hugr-passes/src/lib.rs
@@ -1,7 +1,10 @@
 //! Compilation passes acting on the HUGR program representation.
 
 pub mod const_fold;
+pub mod force_order;
 mod half_node;
 pub mod merge_bbs;
 pub mod nest_cfgs;
 pub mod validation;
+
+pub use force_order::{force_order, force_order_by_key};