diff --git a/differential-dataflow/examples/columnar/main.rs b/differential-dataflow/examples/columnar/main.rs
index 966bb7105..dc4daf24f 100644
--- a/differential-dataflow/examples/columnar/main.rs
+++ b/differential-dataflow/examples/columnar/main.rs
@@ -143,7 +143,7 @@ mod reachability {
 
             // join_traces with ValColBuilder: produces Stream<_, RecordedUpdates<...>>.
             let proposed =
-                join_traces::<_, _, _, ValColBuilder<(Node, (), IterTime, Diff)>>(
+                join_traces::<_, _, _, _, ValColBuilder<(Node, (), IterTime, Diff)>>(
                     edges_arr,
                     reach_arr,
                     |_src, dst, (), time, d1, d2, session| {
diff --git a/differential-dataflow/src/operators/arrange/arrangement.rs b/differential-dataflow/src/operators/arrange/arrangement.rs
index b5261f2a7..6bbce6419 100644
--- a/differential-dataflow/src/operators/arrange/arrangement.rs
+++ b/differential-dataflow/src/operators/arrange/arrangement.rs
@@ -227,26 +227,28 @@ impl<'scope, Tr1: TraceReader<Batch: Navigable>+'static> Arranged<'scope, Tr1> {
     /// A convenience method to join and produce `VecCollection` output.
     ///
     /// Avoid this method, as it is likely to evolve into one without the `VecCollection` opinion.
-    pub fn join_core<Tr2,I,L,R1,R2>(self, other: Arranged<'scope, Tr2>, mut result: L) -> VecCollection<'scope, Tr1::Time,I::Item,<R1 as Multiply<R2>>::Output>
+    pub fn join_core<Tr2,I,L,R1,R2,KC>(self, other: Arranged<'scope, Tr2>, mut result: L) -> VecCollection<'scope, Tr1::Time,I::Item,<R1 as Multiply<R2>>::Output>
     where
         Tr2: TraceReader<Batch: Navigable, Time=Tr1::Time>+Clone+'static,
         // Pin the cursor diffs to named params `R1`/`R2`: a `Multiply` bound on a projection
         // does not connect to its use-site (the solver normalizes the use but not the bound's
         // subject), so we constrain plain params instead.
-        BatchCursor<Tr1>: Cursor<Diff = R1, Time = Tr1::Time>,
+        BatchCursor<Tr1>: Cursor<Diff = R1, Time = Tr1::Time, KeyContainer = KC>,
         BatchCursor<Tr2>: Cursor<Diff = R2, Time = Tr1::Time>,
-        for<'a> BatchCursor<Tr2>: Cursor<Key<'a> = BatchKey<'a, Tr1>>,
+        KC: BatchContainer,
+        for<'a> BatchCursor<Tr1>: Cursor<Key<'a> = KC::ReadItem<'a>>,
+        for<'a> BatchCursor<Tr2>: Cursor<Key<'a> = KC::ReadItem<'a>>,
         R1: Multiply<R2, Output: Semigroup+'static> + Clone,
         I: IntoIterator<Item: Data>,
-        L: FnMut(BatchKey<'_, Tr1>,BatchVal<'_, Tr1>,BatchVal<'_, Tr2>)->I+'static
+        L: FnMut(KC::ReadItem<'_>,BatchVal<'_, Tr1>,BatchVal<'_, Tr2>)->I+'static
     {
-        let mut result = move |k: BatchKey<'_, Tr1>, v1: BatchVal<'_, Tr1>, v2: BatchVal<'_, Tr2>, t: Tr1::Time, r1: &R1, r2: &R2| {
+        let mut result = move |k: KC::ReadItem<'_>, v1: BatchVal<'_, Tr1>, v2: BatchVal<'_, Tr2>, t: Tr1::Time, r1: &R1, r2: &R2| {
             let r = (r1.clone()).multiply(r2);
             result(k, v1, v2).into_iter().map(move |d| (d, t.clone(), r.clone()))
         };
 
         use crate::operators::join::join_traces;
-        join_traces::<_, _, _, crate::consolidation::ConsolidatingContainerBuilder<_>>(
+        join_traces::<_, _, _, _, crate::consolidation::ConsolidatingContainerBuilder<_>>(
             self,
             other,
             move |k, v1, v2, t, d1, d2, c| {
diff --git a/differential-dataflow/src/operators/join.rs b/differential-dataflow/src/operators/join.rs
index 58b42e6f3..023c8648d 100644
--- a/differential-dataflow/src/operators/join.rs
+++ b/differential-dataflow/src/operators/join.rs
@@ -17,8 +17,9 @@ use timely::dataflow::operators::Capability;
 
 use crate::lattice::Lattice;
 use crate::operators::arrange::Arranged;
-use crate::trace::{BatchCursor, BatchDiff, BatchKey, BatchReader, BatchVal, Cursor, Navigable, TraceReader};
+use crate::trace::{BatchCursor, BatchDiff, BatchReader, BatchVal, Cursor, Navigable, TraceReader};
 use crate::trace::cursor::cursor_list;
+use crate::trace::implementations::containers::BatchContainer;
 use crate::operators::ValueHistory;
 
 /// A type that can manage the joining of lists of batches.
@@ -59,13 +60,15 @@ pub enum Fresh {
 /// The "correctness" of this method depends heavily on the behavior of the supplied `result` function.
 ///
 /// [`AsCollection`]: crate::collection::AsCollection
-pub fn join_traces<'scope, Tr1, Tr2, L, CB>(arranged1: Arranged<'scope, Tr1>, arranged2: Arranged<'scope, Tr2>, result: L) -> Stream<'scope, Tr1::Time, CB::Container>
+pub fn join_traces<'scope, Tr1, Tr2, KC, L, CB>(arranged1: Arranged<'scope, Tr1>, arranged2: Arranged<'scope, Tr2>, result: L) -> Stream<'scope, Tr1::Time, CB::Container>
 where
     Tr1: TraceReader<Batch: Navigable>+'static,
     Tr2: TraceReader<Batch: Navigable, Time = Tr1::Time>+'static,
-    BatchCursor<Tr1>: Cursor<Time = Tr1::Time>,
-    for<'a> BatchCursor<Tr2>: Cursor<Key<'a>=BatchKey<'a, Tr1>, Time = Tr1::Time>,
-    L: FnMut(BatchKey<'_, Tr1>,BatchVal<'_, Tr1>,BatchVal<'_, Tr2>,Tr1::Time,&BatchDiff<Tr1>,&BatchDiff<Tr2>,&mut CB)+'static,
+    KC: BatchContainer,
+    BatchCursor<Tr1>: Cursor<Time = Tr1::Time, KeyContainer = KC>,
+    for<'a> BatchCursor<Tr1>: Cursor<Key<'a> = KC::ReadItem<'a>>,
+    for<'a> BatchCursor<Tr2>: Cursor<Key<'a> = KC::ReadItem<'a>, Time = Tr1::Time>,
+    L: FnMut(KC::ReadItem<'_>,BatchVal<'_, Tr1>,BatchVal<'_, Tr2>,Tr1::Time,&BatchDiff<Tr1>,&BatchDiff<Tr2>,&mut CB)+'static,
     CB: ContainerBuilder<Container: Default> + 'static,
 {
     join_with_tactic(arranged1, arranged2, cursors::CursorTactic::<Tr1::Batch, Tr2::Batch, _, CB>::new(result))
diff --git a/interactive/src/backend/col.rs b/interactive/src/backend/col.rs
index d87a64cb0..1948c55d1 100644
--- a/interactive/src/backend/col.rs
+++ b/interactive/src/backend/col.rs
@@ -161,7 +161,7 @@ mod render {
         use differential_dataflow::operators::join::join_traces;
         use differential_dataflow::collection::AsCollection;
         use super::columnar::ValColBuilder;
-        let stream = join_traces::<_, _, _, ValColBuilder<DdirUpdate>>(l, r, move |k, v1, v2, t, d1, d2, c| {
+        let stream = join_traces::<_, _, _, _, ValColBuilder<DdirUpdate>>(l, r, move |k, v1, v2, t, d1, d2, c| {
             use differential_dataflow::difference::Multiply;
             let d = d1.clone().multiply(d2);
             let i = [k.as_slice(), v1.as_slice(), v2.as_slice()];