diff --git a/src/compute/src/render/join/mz_join_core.rs b/src/compute/src/render/join/mz_join_core.rs
index 206b5ccb12cca..be27d996a68e3 100644
--- a/src/compute/src/render/join/mz_join_core.rs
+++ b/src/compute/src/render/join/mz_join_core.rs
@@ -198,10 +198,10 @@ where
                                         trace2.cursor_through(acknowledged2.borrow()).unwrap();
                                     let batch1_cursor = batch1.cursor();
                                     todo1.push_back(Deferred::new(
-                                        trace2_cursor,
-                                        trace2_storage,
                                         batch1_cursor,
                                         batch1.clone(),
+                                        trace2_cursor,
+                                        trace2_storage,
                                         capability.clone(),
                                     ));
                                 }
@@ -273,27 +273,13 @@ where
                     // which results in unintentionally quadratic processing time (each batch of either
                     // input must scan all batches from the other input).
 
-                    let mut work_result = |k: &Tr1::Key,
-                                           v1: &Tr1::Val,
-                                           v2: &Tr2::Val,
-                                           t: &G::Timestamp,
-                                           r1: &Tr1::R,
-                                           r2: &Tr2::R| {
-                        let t = t.clone();
-                        let r = r1.clone().multiply(r2);
-                        result(k, v1, v2)
-                            .into_iter()
-                            .map(move |d| (d, t.clone(), r.clone()))
-                    };
-
                     // Perform some amount of outstanding work.
                     let mut fuel = 1_000_000;
                     while !todo1.is_empty() && fuel > 0 {
-                        todo1.front_mut().unwrap().work(
-                            output,
-                            |k, v2, v1, t, r2, r1| work_result(k, v1, v2, t, r1, r2),
-                            &mut fuel,
-                        );
+                        todo1
+                            .front_mut()
+                            .unwrap()
+                            .work(output, &mut result, &mut fuel);
                         if !todo1.front().unwrap().work_remains() {
                             todo1.pop_front();
                         }
@@ -305,7 +291,7 @@ where
                         todo2
                             .front_mut()
                             .unwrap()
-                            .work(output, &mut work_result, &mut fuel);
+                            .work(output, &mut result, &mut fuel);
                         if !todo2.front().unwrap().work_remains() {
                             todo2.pop_front();
                         }
@@ -373,10 +359,10 @@ where
     C1: Cursor<Key = Row, Val = Row, Time = T, R = Diff>,
     C2: Cursor<Key = Row, Val = Row, Time = T, R = Diff>,
 {
-    trace: C1,
-    trace_storage: C1::Storage,
-    batch: C2,
-    batch_storage: C2::Storage,
+    cursor1: C1,
+    storage1: C1::Storage,
+    cursor2: C2,
+    storage2: C2::Storage,
     capability: Capability<T>,
     done: bool,
     temp: Vec<(D, T, Diff)>,
@@ -390,17 +376,17 @@ where
     D: Data,
 {
     fn new(
-        trace: C1,
-        trace_storage: C1::Storage,
-        batch: C2,
-        batch_storage: C2::Storage,
+        cursor1: C1,
+        storage1: C1::Storage,
+        cursor2: C2,
+        storage2: C2::Storage,
         capability: Capability<T>,
     ) -> Self {
         Deferred {
-            trace,
-            trace_storage,
-            batch,
-            batch_storage,
+            cursor1,
+            storage1,
+            cursor2,
+            storage2,
             capability,
             done: false,
             temp: Vec::new(),
@@ -415,46 +401,50 @@ where
     fn work<L, I>(
         &mut self,
         output: &mut OutputHandle<T, (D, T, Diff), Tee<T, (D, T, Diff)>>,
-        mut logic: L,
+        mut result: L,
         fuel: &mut usize,
     ) where
-        I: IntoIterator<Item = (D, T, Diff)>,
-        L: FnMut(&C1::Key, &C1::Val, &C2::Val, &T, &C1::R, &C2::R) -> I,
+        I: IntoIterator<Item = D>,
+        L: FnMut(&C1::Key, &C1::Val, &C2::Val) -> I,
     {
         let meet = self.capability.time();
 
         let mut session = output.session(&self.capability);
 
-        let trace_storage = &self.trace_storage;
-        let batch_storage = &self.batch_storage;
+        let storage1 = &self.storage1;
+        let storage2 = &self.storage2;
 
-        let trace = &mut self.trace;
-        let batch = &mut self.batch;
+        let cursor1 = &mut self.cursor1;
+        let cursor2 = &mut self.cursor2;
 
         let temp = &mut self.temp;
 
-        while batch.key_valid(batch_storage) && trace.key_valid(trace_storage) {
-            match trace.key(trace_storage).cmp(batch.key(batch_storage)) {
-                Ordering::Less => trace.seek_key(trace_storage, batch.key(batch_storage)),
-                Ordering::Greater => batch.seek_key(batch_storage, trace.key(trace_storage)),
+        while cursor1.key_valid(storage1) && cursor2.key_valid(storage2) {
+            match cursor1.key(storage1).cmp(cursor2.key(storage2)) {
+                Ordering::Less => cursor1.seek_key(storage1, cursor2.key(storage2)),
+                Ordering::Greater => cursor2.seek_key(storage2, cursor1.key(storage1)),
                 Ordering::Equal => {
                     assert_eq!(temp.len(), 0);
 
                     // Populate `temp` with the results, as long as fuel remains.
-                    let key = batch.key(batch_storage);
-                    while let Some(val1) = trace.get_val(trace_storage) {
-                        while let Some(val2) = batch.get_val(batch_storage) {
-                            trace.map_times(trace_storage, |time1, diff1| {
+                    let key = cursor2.key(storage2);
+                    while let Some(val1) = cursor1.get_val(storage1) {
+                        while let Some(val2) = cursor2.get_val(storage2) {
+                            cursor1.map_times(storage1, |time1, diff1| {
                                 let time1 = time1.join(meet);
-                                batch.map_times(batch_storage, |time2, diff2| {
+                                cursor2.map_times(storage2, |time2, diff2| {
                                     let time = time1.join(time2);
-                                    temp.extend(logic(key, val1, val2, &time, diff1, diff2))
+                                    let diff = diff1.multiply(diff2);
+                                    let results = result(key, val1, val2)
+                                        .into_iter()
+                                        .map(|d| (d, time.clone(), diff.clone()));
+                                    temp.extend(results);
                                 });
                             });
-                            batch.step_val(batch_storage);
+                            cursor2.step_val(storage2);
                         }
-                        batch.rewind_vals(batch_storage);
-                        trace.step_val(trace_storage);
+                        cursor1.step_val(storage1);
+                        cursor2.rewind_vals(storage2);
 
                         // TODO: This consolidation is optional, and it may not be very
                         //       helpful. We might try harder to understand whether we
@@ -472,8 +462,8 @@ where
                         }
                     }
 
-                    batch.step_key(batch_storage);
-                    trace.step_key(trace_storage);
+                    cursor1.step_key(storage1);
+                    cursor2.step_key(storage2);
                 }
             }
         }