diff --git a/src/compute-types/src/plan/lowering.rs b/src/compute-types/src/plan/lowering.rs
index c8b9fe5356932..0c5cfb3f6b61c 100644
--- a/src/compute-types/src/plan/lowering.rs
+++ b/src/compute-types/src/plan/lowering.rs
@@ -548,8 +548,6 @@ impl Context {
                 equivalences,
                 implementation,
             } => {
-                let input_mapper = JoinInputMapper::new(inputs);
-
                 // Plan each of the join inputs independently.
                 // The `plans` get surfaced upwards, and the `input_keys` should
                 // be used as part of join planning / to validate the existing
@@ -564,6 +562,9 @@ impl Context {
                     input_keys.push(keys);
                 }
 
+                let input_mapper =
+                    JoinInputMapper::new_from_input_arities(input_arities.iter().copied());
+
                 // Extract temporal predicates as joins cannot currently absorb them.
                 let (plan, missing) = match implementation {
                     IndexedFilter(_coll_id, _idx_id, key, _val) => {
diff --git a/src/expr/src/linear.rs b/src/expr/src/linear.rs
index 51195f264694f..c3ad2be55be33 100644
--- a/src/expr/src/linear.rs
+++ b/src/expr/src/linear.rs
@@ -329,6 +329,8 @@ impl MapFilterProject {
                 let (mfp, expr) = Self::extract_from_expression(input);
                 (mfp.project(outputs.iter().cloned()), expr)
             }
+            // TODO: The recursion is quadratic in the number of Map/Filter/Project operators due to
+            // this call to `arity()`.
             x => (Self::new(x.arity()), x),
         }
     }
diff --git a/src/expr/src/relation.rs b/src/expr/src/relation.rs
index d75dad187a93f..85b48910dad67 100644
--- a/src/expr/src/relation.rs
+++ b/src/expr/src/relation.rs
@@ -1787,22 +1787,21 @@ impl MirRelationExpr {
             .unzip();
         assert_eq!(keys_and_values.arity() - self.arity(), data.len());
         self.let_in(id_gen, |_id_gen, get_keys| {
+            let get_keys_arity = get_keys.arity();
             Ok(MirRelationExpr::join(
                 vec![
                     // all the missing keys (with count 1)
                     keys_and_values
-                        .distinct_by((0..get_keys.arity()).collect())
+                        .distinct_by((0..get_keys_arity).collect())
                         .negate()
                         .union(get_keys.clone().distinct()),
                     // join with keys to get the correct counts
                     get_keys.clone(),
                 ],
-                (0..get_keys.arity())
-                    .map(|i| vec![(0, i), (1, i)])
-                    .collect(),
+                (0..get_keys_arity).map(|i| vec![(0, i), (1, i)]).collect(),
             )
             // get rid of the extra copies of columns from keys
-            .project((0..get_keys.arity()).collect())
+            .project((0..get_keys_arity).collect())
             // This join is logically equivalent to
             // `.map(<default_expr>)`, but using a join allows for
             // potential predicate pushdown and elision in the
diff --git a/src/sql/src/plan/lowering.rs b/src/sql/src/plan/lowering.rs
index e6a214d265e60..b7e16f481acbd 100644
--- a/src/sql/src/plan/lowering.rs
+++ b/src/sql/src/plan/lowering.rs
@@ -1574,12 +1574,14 @@ impl HirScalarExpr {
                 let inner_arity = get_inner.arity();
                 let mut total_arity = inner_arity;
                 let mut join_inputs = vec![get_inner];
+                let mut join_input_arities = vec![inner_arity];
                 for (expr, subquery) in subqueries.into_iter() {
                     // Avoid lowering duplicated subqueries
                     if !subquery_map.contains_key(&expr) {
                         let subquery_arity = subquery.arity();
                         assert_eq!(subquery_arity, inner_arity + 1);
                         join_inputs.push(subquery);
+                        join_input_arities.push(subquery_arity);
                         total_arity += subquery_arity;
 
                         // Column with the value of the subquery
@@ -1589,7 +1591,8 @@ impl HirScalarExpr {
                 // Each subquery projects all the columns of the outer context (distinct_inner)
                 // plus 1 column, containing the result of the subquery. Those columns must be
                 // joined with the outer/main relation (get_inner).
-                let input_mapper = mz_expr::JoinInputMapper::new(&join_inputs);
+                let input_mapper =
+                    mz_expr::JoinInputMapper::new_from_input_arities(join_input_arities);
                 let equivalences = (0..inner_arity)
                     .map(|col| {
                         join_inputs