diff --git a/core-relations/src/action/mod.rs b/core-relations/src/action/mod.rs
index 3bc4d5803..abbe90b05 100644
--- a/core-relations/src/action/mod.rs
+++ b/core-relations/src/action/mod.rs
@@ -279,6 +279,28 @@ impl Bindings {
     }
 }
 
+fn single_external_borrowed_window(
+    instrs: &[Instr],
+) -> Option<(ExternalFunctionId, Variable, usize, Variable)> {
+    match instrs {
+        [Instr::External { func, args, dst }] => {
+            let mut start = None;
+            for (idx, arg) in args.iter().enumerate() {
+                let QueryEntry::Var(v) = arg else {
+                    return None;
+                };
+                if idx == 0 {
+                    start = Some(*v);
+                } else if v.index() != start?.index() + idx {
+                    return None;
+                }
+            }
+            start.map(|start| (*func, start, args.len(), *dst))
+        }
+        _ => None,
+    }
+}
+
 /// A binding that has been extracted from a [`Bindings`] struct via the [`Bindings::take`] method.
 ///
 /// This allows for a variable's contents to be read while the [`Bindings`] struct has been
@@ -603,6 +625,33 @@ impl ExecutionState<'_> {
             bindings.matches = 1;
         }
 
+        if let Some((func, start, len, dst)) = single_external_borrowed_window(instrs) {
+            let matches = bindings.matches;
+            let mut out: Pooled<Vec<Value>> = with_pool_set(|ps| ps.get());
+            out.resize(matches, Value::stale());
+            let mut transposed: Pooled<Vec<Value>> = with_pool_set(|ps| ps.get());
+            transposed.resize(matches * len, Value::stale());
+            let start_index = start.index();
+            let mut succeeded = 0usize;
+            for row in 0..matches {
+                for col in 0..len {
+                    transposed[row * len + col] =
+                        bindings[Variable::from_usize(start_index + col)][row];
+                }
+                if self.should_stop() {
+                    break;
+                }
+                if let Some(value) =
+                    self.call_external_func(func, &transposed[row * len..(row + 1) * len])
+                {
+                    out[row] = value;
+                    succeeded += 1;
+                }
+            }
+            bindings.insert(dst, &out);
+            return succeeded;
+        }
+
         // Vectorized execution for larger batch sizes
         let mut mask = with_pool_set(|ps| Mask::new(0..bindings.matches, ps));
         for instr in instrs {
diff --git a/core-relations/src/action/tests.rs b/core-relations/src/action/tests.rs
index 4f1c0484b..363014ef0 100644
--- a/core-relations/src/action/tests.rs
+++ b/core-relations/src/action/tests.rs
@@ -1,5 +1,7 @@
 use crate::{
     action::mask::{IterResult, ValueSource},
+    free_join::Variable,
+    numeric_id::NumericId,
     pool::{PoolSet, with_pool_set},
 };
 
@@ -148,3 +150,40 @@ fn test_early_stop_multiple_clones() {
     assert!(state2.should_stop());
     assert!(state3.should_stop());
 }
+
+#[test]
+fn run_instrs_single_external_borrowed_window_executes() {
+    let mut db = crate::free_join::Database::default();
+    let sum = db.add_external_function(Box::new(crate::make_external_func(|_, args| {
+        let [x, y] = args else { panic!() };
+        Some(crate::common::Value::from_usize(
+            (x.rep() + y.rep()) as usize,
+        ))
+    })));
+    let mut state = crate::action::ExecutionState::new(db.read_only_view(), Default::default());
+    let mut bindings = super::Bindings::new(8);
+    bindings.insert(
+        Variable::from_usize(0),
+        &[crate::table_shortcuts::v(1), crate::table_shortcuts::v(2)],
+    );
+    bindings.insert(
+        Variable::from_usize(1),
+        &[crate::table_shortcuts::v(10), crate::table_shortcuts::v(20)],
+    );
+
+    let instrs = vec![super::Instr::External {
+        func: sum,
+        args: vec![
+            Variable::from_usize(0).into(),
+            Variable::from_usize(1).into(),
+        ],
+        dst: Variable::from_usize(2),
+    }];
+
+    let succeeded = state.run_instrs(&instrs, &mut bindings);
+    assert_eq!(succeeded, 2);
+    assert_eq!(
+        &bindings[Variable::from_usize(2)],
+        &[crate::table_shortcuts::v(11), crate::table_shortcuts::v(22)]
+    );
+}
diff --git a/core-relations/src/query.rs b/core-relations/src/query.rs
index e66c2a29e..ce8c3f2c8 100644
--- a/core-relations/src/query.rs
+++ b/core-relations/src/query.rs
@@ -1,6 +1,6 @@
 //! APIs for building a query of a database.
 
-use std::{iter::once, sync::Arc};
+use std::{iter::once, mem, sync::Arc};
 
 use crate::numeric_id::{DenseIdMap, IdVec, NumericId, define_id};
 use smallvec::SmallVec;
@@ -444,7 +444,71 @@ impl RuleBuilder<'_, '_> {
         }
     }
 
+    fn normalize_single_external_layout(&mut self) {
+        let Some((arg_vars, dst_var)) = single_external_signature(&self.qb.instrs) else {
+            return;
+        };
+
+        let mut preferred = SmallVec::<[Variable; 4]>::new();
+        preferred.extend(arg_vars.iter().copied());
+        preferred.extend(
+            self.qb
+                .query
+                .var_info
+                .iter()
+                .map(|(var, _)| var)
+                .filter(|var| !arg_vars.contains(var)),
+        );
+
+        let current =
+            SmallVec::<[Variable; 4]>::from_iter(self.qb.query.var_info.iter().map(|(var, _)| var));
+        if preferred == current {
+            return;
+        }
+
+        let mut remap = DenseIdMap::with_capacity(self.qb.query.var_info.n_ids());
+        for (idx, old_var) in preferred.iter().enumerate() {
+            remap.insert(*old_var, Variable::from_usize(idx));
+        }
+
+        let mut old_var_info = mem::take(&mut self.qb.query.var_info);
+        for old_var in preferred {
+            self.qb.query.var_info.push(
+                old_var_info
+                    .take(old_var)
+                    .expect("all vars must be present"),
+            );
+        }
+
+        for (_, atom) in self.qb.query.atoms.iter_mut() {
+            let old_var_to_column = mem::take(&mut atom.var_to_column);
+            atom.var_to_column = old_var_to_column
+                .into_iter()
+                .map(|(var, col)| (remap[var], col))
+                .collect();
+            for (_, var) in atom.column_to_var.iter_mut() {
+                *var = remap[*var];
+            }
+        }
+
+        let [Instr::External { args, dst, .. }] = self.qb.instrs.as_mut_slice() else {
+            unreachable!("single_external_signature should guarantee the instruction shape");
+        };
+        args.iter_mut()
+            .for_each(|entry| remap_query_entry(entry, &remap));
+        *dst = remap[dst_var];
+    }
+
+    fn plan_single_external_layout(&mut self) {
+        if !matches!(self.qb.instrs.as_slice(), [Instr::External { .. }]) {
+            return;
+        }
+
+        self.normalize_single_external_layout();
+    }
+
     pub fn build_with_description(mut self, desc: impl Into<String>) -> RuleId {
+        self.plan_single_external_layout();
         let var_info = &self.qb.query.var_info;
         let symbol_map = self.build_symbol_map();
         // Generate an id for our actions and slot them in.
@@ -769,6 +833,30 @@ impl RuleBuilder<'_, '_> {
     }
 }
 
+fn single_external_signature(instrs: &[Instr]) -> Option<(SmallVec<[Variable; 4]>, Variable)> {
+    let [Instr::External { args, dst, .. }] = instrs else {
+        return None;
+    };
+
+    let mut vars = SmallVec::<[Variable; 4]>::new();
+    for arg in args {
+        let QueryEntry::Var(var) = arg else {
+            return None;
+        };
+        if vars.contains(var) {
+            return None;
+        }
+        vars.push(*var);
+    }
+    Some((vars, *dst))
+}
+
+fn remap_query_entry(entry: &mut QueryEntry, remap: &DenseIdMap<Variable, Variable>) {
+    if let QueryEntry::Var(var) = entry {
+        *var = remap[*var];
+    }
+}
+
 #[derive(Debug, Clone)]
 pub(crate) struct Atom {
     pub(crate) table: TableId,
diff --git a/core-relations/src/tests.rs b/core-relations/src/tests.rs
index 59b623227..dafe788a2 100644
--- a/core-relations/src/tests.rs
+++ b/core-relations/src/tests.rs
@@ -122,6 +122,59 @@ fn basic_query() {
     assert_eq!(res, Vec::from_iter((0..10).chain([13, 17].into_iter())));
 }
 
+#[test]
+fn single_external_rule_normalizes_gap_vars_into_consecutive_window() {
+    let mut db = Database::default();
+    let tuple4 = db.add_table(
+        SortedWritesTable::new(4, 4, None, vec![], Box::new(|_, _, _, _| false)),
+        iter::empty(),
+        iter::empty(),
+    );
+    let echo = db.add_external_function(Box::new(make_external_func(|_, args| {
+        args.first().copied()
+    })));
+
+    let mut rsb = RuleSetBuilder::new(&mut db);
+    let mut query = rsb.new_rule();
+    let a = query.new_var_named("a");
+    let b = query.new_var_named("b");
+    let c = query.new_var_named("c");
+    let d = query.new_var_named("d");
+    query
+        .add_atom(tuple4, &[a.into(), b.into(), c.into(), d.into()], &[])
+        .unwrap();
+    let mut rule = query.build();
+    let _ = rule
+        .call_external(echo, &[a.into(), b.into(), d.into()])
+        .unwrap();
+    let rule_id = rule.build_with_description("single_external_gap");
+    let rule_set = rsb.build();
+
+    let (_, _, _, action_id) = rule_set.plans.get(rule_id).unwrap();
+    let action = &rule_set.actions[*action_id];
+    let [crate::action::Instr::External { args, .. }] = action.instrs.as_ref().as_slice() else {
+        panic!("expected single external instruction");
+    };
+
+    let vars: Vec<_> = args
+        .iter()
+        .map(|arg| match arg {
+            crate::action::QueryEntry::Var(var) => *var,
+            crate::action::QueryEntry::Const(_) => panic!("expected var-only external args"),
+        })
+        .collect();
+
+    assert_eq!(
+        vars,
+        vec![
+            crate::free_join::Variable::from_usize(0),
+            crate::free_join::Variable::from_usize(1),
+            crate::free_join::Variable::from_usize(2)
+        ],
+        "eligible single-external rules should normalize arg vars into a consecutive window",
+    );
+}
+
 #[test]
 fn line_graph_1_fj_puresize() {
     line_graph_1_test(PlanStrategy::PureSize);