diff --git a/src/flow/flow.rs b/src/flow/flow.rs
index f8c3596..bd3838d 100644
--- a/src/flow/flow.rs
+++ b/src/flow/flow.rs
@@ -2,14 +2,15 @@ use crate::flow::adjacencies::Adjacencies;
 use crate::flow::{node_as_address, node_as_token_edge, Node};
 use crate::types::{Address, Edge, U256};
 use std::cmp::min;
-use std::collections::HashMap;
 use std::collections::VecDeque;
+use std::collections::{BTreeMap, HashMap, HashSet};
 use std::fmt::Write;
 
 pub fn compute_flow(
     source: &Address,
     sink: &Address,
     edges: &HashMap<Address, Vec<Edge>>,
+    requested_flow: U256,
     max_distance: Option<u64>,
 ) -> (U256, Vec<Edge>) {
     let mut adjacencies = Adjacencies::new(edges);
@@ -45,9 +46,13 @@ pub fn compute_flow(
         }
     }
 
-    // TODO prune
-
     println!("Max flow: {flow}");
+
+    if flow > requested_flow {
+        let still_to_prune = prune_flow(source, sink, flow - requested_flow, &mut used_edges);
+        flow = requested_flow + still_to_prune;
+    }
+
     let transfers = if flow == U256::from(0) {
         vec![]
     } else {
@@ -137,6 +142,233 @@ fn to_dot(
     out
 }
 
+fn prune_flow(
+    source: &Address,
+    sink: &Address,
+    mut flow_to_prune: U256,
+    used_edges: &mut HashMap<Node, HashMap<Node, U256>>,
+) -> U256 {
+    // Note the path length is negative to sort by longest shortest path first.
+    let edges_by_path_length = compute_edges_by_path_length(source, sink, used_edges);
+
+    for edges_here in edges_by_path_length.values() {
+        //println!("Shorter path.");
+        // As long as `edges` contain an edge with smaller weight than the weight still to prune:
+        //   take the smallest such edge and prune it.
+        while flow_to_prune > U256::from(0) && !edges_here.is_empty() {
+            //println!("Still to prune: {}", flow_to_prune);
+            if let Some((s, t)) = smallest_edge_in_set(used_edges, edges_here) {
+                if used_edges[&s][&t] > flow_to_prune {
+                    break;
+                };
+                flow_to_prune = prune_edge(used_edges, (&s, &t), flow_to_prune);
+            } else {
+                break;
+            }
+        }
+    }
+    // If there is still flow to prune, take the first element in edgesByPathLength
+    // and partially prune its path.
+    if flow_to_prune > U256::from(0) {
+        //println!("Final stage: Still to prune: {}", flow_to_prune);
+        for edges_here in edges_by_path_length.values() {
+            for (a, b) in edges_here {
+                if !used_edges.contains_key(a) || !used_edges[a].contains_key(b) {
+                    continue;
+                }
+                flow_to_prune = prune_edge(used_edges, (a, b), flow_to_prune);
+                if flow_to_prune == U256::from(0) {
+                    return U256::from(0);
+                }
+            }
+            if flow_to_prune == U256::from(0) {
+                return U256::from(0);
+            }
+        }
+    }
+    flow_to_prune
+}
+
+/// Returns a map from the negative shortest path length to the edge.
+/// The shortest path length is negative so that it is sorted by
+/// longest paths first - those are the ones we want to eliminate first.
+fn compute_edges_by_path_length(
+    source: &Address,
+    sink: &Address,
+    used_edges: &HashMap<Node, HashMap<Node, U256>>,
+) -> BTreeMap<i64, HashSet<(Node, Node)>> {
+    let mut result = BTreeMap::<i64, HashSet<(Node, Node)>>::new();
+    let from_source = distance_from_source(&Node::Node(*source), used_edges);
+    let to_sink = distance_to_sink(&Node::Node(*sink), used_edges);
+    for (s, edges) in used_edges {
+        for t in edges.keys() {
+            let path_length = from_source[s] + 1 + to_sink[t];
+            result
+                .entry(-path_length)
+                .or_default()
+                .insert((s.clone(), t.clone()));
+        }
+    }
+    result
+}
+
+fn distance_from_source(
+    source: &Node,
+    used_edges: &HashMap<Node, HashMap<Node, U256>>,
+) -> HashMap<Node, i64> {
+    let mut distances = HashMap::<Node, i64>::new();
+    let mut to_process = VecDeque::<Node>::new();
+    distances.insert(source.clone(), 0);
+    to_process.push_back(source.clone());
+
+    while let Some(n) = to_process.pop_front() {
+        for (t, capacity) in used_edges.get(&n).unwrap_or(&HashMap::new()) {
+            if *capacity > U256::from(0) && !distances.contains_key(t) {
+                distances.insert(t.clone(), distances[&n] + 1);
+                to_process.push_back(t.clone());
+            }
+        }
+    }
+
+    distances
+}
+
+fn distance_to_sink(
+    sink: &Node,
+    used_edges: &HashMap<Node, HashMap<Node, U256>>,
+) -> HashMap<Node, i64> {
+    distance_from_source(sink, &reverse_edges(used_edges))
+}
+
+fn reverse_edges(
+    used_edges: &HashMap<Node, HashMap<Node, U256>>,
+) -> HashMap<Node, HashMap<Node, U256>> {
+    let mut reversed: HashMap<Node, HashMap<Node, U256>> = HashMap::new();
+    for (n, edges) in used_edges {
+        for (t, capacity) in edges {
+            reversed
+                .entry(t.clone())
+                .or_default()
+                .insert(n.clone(), *capacity);
+        }
+    }
+    reversed
+}
+
+fn smallest_edge_in_set(
+    all_edges: &HashMap<Node, HashMap<Node, U256>>,
+    edge_set: &HashSet<(Node, Node)>,
+) -> Option<(Node, Node)> {
+    if let Some((a, b, _)) = edge_set
+        .iter()
+        .map(|(a, b)| {
+            let capacity = if let Some(out) = all_edges.get(a) {
+                if let Some(capacity) = out.get(b) {
+                    assert!(*capacity != U256::from(0));
+                    Some(capacity)
+                } else {
+                    None
+                }
+            } else {
+                None
+            };
+            (a, b, capacity)
+        })
+        .filter(|(_, _, capacity)| capacity.is_some())
+        .min_by_key(|(_, _, capacity)| capacity.unwrap())
+    {
+        Some((a.clone(), b.clone()))
+    } else {
+        None
+    }
+}
+
+fn smallest_edge_from(
+    used_edges: &HashMap<Node, HashMap<Node, U256>>,
+    n: &Node,
+) -> Option<(Node, U256)> {
+    used_edges
+        .get(n)
+        .and_then(|out| {
+            out.iter()
+                .min_by_key(|(_, c)| {
+                    assert!(**c != U256::from(0));
+                    *c
+                })
+                .map(|(t, c)| (t.clone(), *c))
+        })
+}
+
+fn smallest_edge_to(
+    used_edges: &HashMap<Node, HashMap<Node, U256>>,
+    n: &Node,
+) -> Option<(Node, U256)> {
+    used_edges
+        .iter()
+        .filter(|(_, out)| out.contains_key(n))
+        .map(|(t, out)| (t, out[n]))
+        .min_by_key(|(_, c)| {
+            assert!(*c != U256::from(0));
+            *c
+        })
+        .map(|(t, c)| (t.clone(), c))
+}
+
+/// Removes the edge (potentially partially), removing a given amount of flow.
+/// Returns the remaining flow to prune if the edge was too small.
+fn prune_edge(
+    used_edges: &mut HashMap<Node, HashMap<Node, U256>>,
+    edge: (&Node, &Node),
+    flow_to_prune: U256,
+) -> U256 {
+    let edge_size = min(flow_to_prune, used_edges[edge.0][edge.1]);
+    reduce_capacity(used_edges, edge, &edge_size);
+    prune_path(used_edges, edge.1, edge_size, PruneDirection::Forwards);
+    prune_path(used_edges, edge.0, edge_size, PruneDirection::Backwards);
+    flow_to_prune - edge_size
+}
+
+fn reduce_capacity(
+    used_edges: &mut HashMap<Node, HashMap<Node, U256>>,
+    (a, b): (&Node, &Node),
+    reduction: &U256,
+) {
+    let out_edges = used_edges.get_mut(a).unwrap();
+    *out_edges.get_mut(b).unwrap() -= *reduction;
+    if out_edges[b] == U256::from(0) {
+        out_edges.remove_entry(b);
+    }
+}
+
+#[derive(Clone, Copy)]
+enum PruneDirection {
+    Forwards,
+    Backwards,
+}
+
+fn prune_path(
+    used_edges: &mut HashMap<Node, HashMap<Node, U256>>,
+    n: &Node,
+    mut flow_to_prune: U256,
+    direction: PruneDirection,
+) {
+    while let Some((next, mut capacity)) = match direction {
+        PruneDirection::Forwards => smallest_edge_from(used_edges, n),
+        PruneDirection::Backwards => smallest_edge_to(used_edges, n),
+    } {
+        capacity = min(flow_to_prune, capacity);
+        match direction {
+            PruneDirection::Forwards => reduce_capacity(used_edges, (n, &next), &capacity),
+            PruneDirection::Backwards => reduce_capacity(used_edges, (&next, n), &capacity),
+        };
+        prune_path(used_edges, &next, capacity, direction);
+        flow_to_prune -= capacity;
+        if flow_to_prune == U256::from(0) {
+            return;
+        }
+    }
+}
+
 fn extract_transfers(
     source: &Address,
     sink: &Address,
@@ -227,7 +459,7 @@ mod test {
             token: t,
             capacity: U256::from(10),
         }]);
-        let flow = compute_flow(&a, &b, &edges, None);
+        let flow = compute_flow(&a, &b, &edges, U256::MAX, None);
         assert_eq!(flow, (U256::from(10), edges[&a].clone()));
     }
 
@@ -248,7 +480,7 @@ mod test {
                 capacity: U256::from(8),
             },
         ]);
-        let flow = compute_flow(&a, &c, &edges, None);
+        let flow = compute_flow(&a, &c, &edges, U256::MAX, None);
         assert_eq!(
             flow,
             (
@@ -300,7 +532,7 @@ mod test {
                 capacity: U256::from(8),
             },
         ]);
-        let mut flow = compute_flow(&a, &d, &edges, None);
+        let mut flow = compute_flow(&a, &d, &edges, U256::MAX, None);
         flow.1.sort();
         assert_eq!(
             flow,
@@ -334,5 +566,27 @@ mod test {
                 ]
             )
         );
+        let mut pruned_flow = compute_flow(&a, &d, &edges, U256::from(6), None);
+        pruned_flow.1.sort();
+        assert_eq!(
+            pruned_flow,
+            (
+                U256::from(6),
+                vec![
+                    Edge {
+                        from: a,
+                        to: b,
+                        token: t1,
+                        capacity: U256::from(6)
+                    },
+                    Edge {
+                        from: b,
+                        to: d,
+                        token: t2,
+                        capacity: U256::from(6)
+                    },
+                ]
+            )
+        );
     }
 }
diff --git a/src/server.rs b/src/server.rs
index 3993e95..7218206 100644
--- a/src/server.rs
+++ b/src/server.rs
@@ -1,6 +1,6 @@
 use crate::flow;
 use crate::io::read_edges_binary;
-use crate::types::{Address, Edge};
+use crate::types::{Address, Edge, U256};
 use json::JsonValue;
 use std::collections::HashMap;
 use std::error::Error;
@@ -61,46 +61,7 @@ fn handle_connection(
         "compute_transfer" => {
             println!("Computing flow");
             let e = edges.read().unwrap().clone();
-
-            socket.write_all(chunked_header().as_bytes())?;
-            let max_distances = if request.params["iterative"].as_bool().unwrap_or_default() {
-                vec![Some(1), Some(2), None]
-            } else {
-                vec![None]
-            };
-            for max_distance in max_distances {
-                let (flow, transfers) = flow::compute_flow(
-                    &Address::from(request.params["from"].to_string().as_str()),
-                    &Address::from(request.params["to"].to_string().as_str()),
-                    //&U256::from(request.params["value"].to_string().as_str()),
-                    e.as_ref(),
-                    max_distance,
-                );
-                println!(
-                    "Computed flow with max distance {:?}: {}",
-                    max_distance, flow
-                );
-                // TODO error handling
-                socket.write_all(
-                    chunked_response(
-                        &(jsonrpc_result(
-                            request.id.clone(),
-                            json::object! {
-                                flow: flow.to_string(),
-                                final: max_distance.is_none(),
-                                transfers: transfers.into_iter().map(|e| json::object! {
-                                    from: e.from.to_string(),
-                                    to: e.to.to_string(),
-                                    token: e.token.to_string(),
-                                    value: e.capacity.to_string()
-                                }).collect::<Vec<_>>(),
-                            },
-                        ) + "\r\n"),
-                    )
-                    .as_bytes(),
-                )?;
-            }
-            socket.write_all(chunked_close().as_bytes())?;
+            compute_transfer(request, e.as_ref(), socket)?;
         }
         "cancel" => {}
         "update_edges" => {}
@@ -110,6 +71,57 @@ fn handle_connection(
     Ok(())
 }
 
+fn compute_transfer(
+    request: JsonRpcRequest,
+    edges: &HashMap<Address, Vec<Edge>>,
+    mut socket: TcpStream,
+) -> Result<(), Box<dyn Error>> {
+    socket.write_all(chunked_header().as_bytes())?;
+    let max_distances = if request.params["iterative"].as_bool().unwrap_or_default() {
+        vec![Some(1), Some(2), None]
+    } else {
+        vec![None]
+    };
+    for max_distance in max_distances {
+        let (flow, transfers) = flow::compute_flow(
+            &Address::from(request.params["from"].to_string().as_str()),
+            &Address::from(request.params["to"].to_string().as_str()),
+            edges,
+            if request.params.has_key("value") {
+                U256::from(request.params["value"].to_string().as_str())
+            } else {
+                U256::MAX
+            },
+            max_distance,
+        );
+        println!(
+            "Computed flow with max distance {:?}: {}",
+            max_distance, flow
+        );
+        // TODO error handling
+        socket.write_all(
+            chunked_response(
+                &(jsonrpc_result(
+                    request.id.clone(),
+                    json::object! {
+                        flow: flow.to_string(),
+                        final: max_distance.is_none(),
+                        transfers: transfers.into_iter().map(|e| json::object! {
+                            from: e.from.to_string(),
+                            to: e.to.to_string(),
+                            token: e.token.to_string(),
+                            value: e.capacity.to_string()
+                        }).collect::<Vec<_>>(),
+                    },
+                ) + "\r\n"),
+            )
+            .as_bytes(),
+        )?;
+    }
+    socket.write_all(chunked_close().as_bytes())?;
+    Ok(())
+}
+
 fn read_request(socket: &mut TcpStream) -> Result<JsonRpcRequest, Box<dyn Error>> {
     let payload = read_payload(socket)?;
     let mut request = json::parse(&String::from_utf8(payload)?)?;
diff --git a/src/types/u256.rs b/src/types/u256.rs
index 27f07ad..bb6ca15 100644
--- a/src/types/u256.rs
+++ b/src/types/u256.rs
@@ -6,9 +6,10 @@ use std::ops::{Add, AddAssign, Neg, Sub, SubAssign};
 pub struct U256([u128; 2]);
 
 impl U256 {
-    pub fn new(high: u128, low: u128) -> U256 {
+    pub const fn new(high: u128, low: u128) -> U256 {
         U256([high, low])
     }
+    pub const MAX: U256 = U256::new(u128::MAX, u128::MAX);
 }
 
 impl From<u128> for U256 {
diff --git a/tests/integration.rs b/tests/integration.rs
index 80dbd2b..a5eb7d5 100644
--- a/tests/integration.rs
+++ b/tests/integration.rs
@@ -1,16 +1,17 @@
-use pathfinder2::flow::compute_flow;
-use pathfinder2::io::read_edges_binary;
-use pathfinder2::types::Address;
+// use pathfinder2::flow::compute_flow;
+// use pathfinder2::io::read_edges_binary;
+// use pathfinder2::types::Address;
 
-#[test]
-fn test_flow() {
-    let edges = read_edges_binary(&"edges.dat".to_string()).unwrap();
-    let transfers = compute_flow(
-        &Address::from("0x8DC7e86fF693e9032A0F41711b5581a04b26Be2E"),
-        &Address::from("0x42cEDde51198D1773590311E2A340DC06B24cB37"),
-        //&Address::from("0x9f5ff18027adbb65a53086cdc09d12ce463dae0b"),
-        &edges,
-        None,
-    );
-    println!("{:?}", transfers);
-}
+// #[test]
+// fn test_flow() {
+//     let edges = read_edges_binary(&"edges.dat".to_string()).unwrap();
+//     let transfers = compute_flow(
+//         &Address::from("0x8DC7e86fF693e9032A0F41711b5581a04b26Be2E"),
+//         &Address::from("0x42cEDde51198D1773590311E2A340DC06B24cB37"),
+//         //&Address::from("0x9f5ff18027adbb65a53086cdc09d12ce463dae0b"),
+//         &edges,
+//         U256::MAX,
+//         None,
+//     );
+//     println!("{:?}", transfers);
+// }