diff --git a/src/operators/arrange/arrangement.rs b/src/operators/arrange/arrangement.rs
index 7995b4397..9856e38e0 100644
--- a/src/operators/arrange/arrangement.rs
+++ b/src/operators/arrange/arrangement.rs
@@ -444,7 +444,7 @@ where
         T2::ValOwned: Data,
         T2::Diff: Abelian,
         T2::Batch: Batch,
-        T2::Builder: Builder<Output=T2::Batch, Item = ((T1::KeyOwned, T2::ValOwned), T2::Time, T2::Diff)>,
+        T2::Builder: Builder<Input = ((T1::KeyOwned, T2::ValOwned), T2::Time, T2::Diff)>,
         L: FnMut(T1::Key<'_>, &[(T1::Val<'_>, T1::Diff)], &mut Vec<(<T2::Cursor as Cursor>::ValOwned, T2::Diff)>)+'static,
     {
         self.reduce_core::<_,T2>(name, move |key, input, output, change| {
@@ -462,7 +462,7 @@ where
         T2: for<'a> Trace<Key<'a>=T1::Key<'a>, Time=T1::Time>+'static,
         T2::ValOwned: Data,
         T2::Batch: Batch,
-        T2::Builder: Builder<Output=T2::Batch, Item = ((T1::KeyOwned, T2::ValOwned), T2::Time, T2::Diff)>,
+        T2::Builder: Builder<Input = ((T1::KeyOwned, T2::ValOwned), T2::Time, T2::Diff)>,
         L: FnMut(T1::Key<'_>, &[(T1::Val<'_>, T1::Diff)], &mut Vec<(<T2::Cursor as Cursor>::ValOwned,T2::Diff)>, &mut Vec<(<T2::Cursor as Cursor>::ValOwned, T2::Diff)>)+'static,
     {
         use crate::operators::reduce::reduce_trace;
diff --git a/src/operators/arrange/upsert.rs b/src/operators/arrange/upsert.rs
index e9d1744ff..4ca9dc9b3 100644
--- a/src/operators/arrange/upsert.rs
+++ b/src/operators/arrange/upsert.rs
@@ -136,7 +136,7 @@ where
     Tr::ValOwned: ExchangeData,
     Tr::Time: TotalOrder+ExchangeData,
     Tr::Batch: Batch,
-    Tr::Builder: Builder<Item = ((Tr::KeyOwned, Tr::ValOwned), Tr::Time, Tr::Diff)>,
+    Tr::Builder: Builder<Input = ((Tr::KeyOwned, Tr::ValOwned), Tr::Time, Tr::Diff)>,
 {
     let mut reader: Option<TraceAgent<Tr>> = None;
 
diff --git a/src/operators/consolidate.rs b/src/operators/consolidate.rs
index 52fb8919f..b67c1c4b8 100644
--- a/src/operators/consolidate.rs
+++ b/src/operators/consolidate.rs
@@ -13,7 +13,7 @@ use crate::difference::Semigroup;
 
 use crate::Data;
 use crate::lattice::Lattice;
-use crate::trace::{Batcher, Builder};
+use crate::trace::Batcher;
 
 /// Methods which require data be arrangeable.
 impl<G, D, R> Collection<G, D, R>
@@ -53,8 +53,7 @@ where
     where
         Tr: crate::trace::Trace<KeyOwned = D,ValOwned = (),Time=G::Timestamp,Diff=R>+'static,
         Tr::Batch: crate::trace::Batch,
-        Tr::Batcher: Batcher<Input=Vec<((D,()),G::Timestamp,R)>, Item = ((D,()),G::Timestamp,R), Time = G::Timestamp>,
-        Tr::Builder: Builder<Item = ((D,()),G::Timestamp,R), Time = G::Timestamp>,
+        Tr::Batcher: Batcher<Input=Vec<((D,()),G::Timestamp,R)>>,
     {
         use crate::operators::arrange::arrangement::Arrange;
         use crate::trace::cursor::MyTrait;
diff --git a/src/operators/reduce.rs b/src/operators/reduce.rs
index 7f322c00e..37d98d8ca 100644
--- a/src/operators/reduce.rs
+++ b/src/operators/reduce.rs
@@ -251,7 +251,7 @@ pub trait ReduceCore<G: Scope, K: ToOwned + ?Sized, V: ToOwned + ?Sized, R: Semi
             T2::ValOwned: Data,
             T2::Diff: Abelian,
             T2::Batch: Batch,
-            T2::Builder: Builder<Output=T2::Batch, Item = ((K::Owned, T2::ValOwned), T2::Time, T2::Diff)>,
+            T2::Builder: Builder<Input = ((K::Owned, T2::ValOwned), T2::Time, T2::Diff)>,
             L: FnMut(&K, &[(&V, R)], &mut Vec<(<T2::Cursor as Cursor>::ValOwned, T2::Diff)>)+'static,
         {
             self.reduce_core::<_,T2>(name, move |key, input, output, change| {
@@ -273,7 +273,7 @@ pub trait ReduceCore<G: Scope, K: ToOwned + ?Sized, V: ToOwned + ?Sized, R: Semi
             T2: for<'a> Trace<Key<'a>=&'a K, Time=G::Timestamp>+'static,
             T2::ValOwned: Data,
             T2::Batch: Batch,
-            T2::Builder: Builder<Output=T2::Batch, Item = ((K::Owned, T2::ValOwned), T2::Time, T2::Diff)>,
+            T2::Builder: Builder<Input = ((K::Owned, T2::ValOwned), T2::Time, T2::Diff)>,
             L: FnMut(&K, &[(&V, R)], &mut Vec<(<T2::Cursor as Cursor>::ValOwned,T2::Diff)>, &mut Vec<(<T2::Cursor as Cursor>::ValOwned, T2::Diff)>)+'static,
             ;
 }
@@ -292,7 +292,7 @@ where
             T2::ValOwned: Data,
             T2: for<'a> Trace<Key<'a>=&'a K, Time=G::Timestamp>+'static,
             T2::Batch: Batch,
-            T2::Builder: Builder<Output=T2::Batch, Item = ((K::Owned, T2::ValOwned), T2::Time, T2::Diff)>,
+            T2::Builder: Builder<Input = ((K::Owned, T2::ValOwned), T2::Time, T2::Diff)>,
             L: FnMut(&K, &[(&V, R)], &mut Vec<(<T2::Cursor as Cursor>::ValOwned,T2::Diff)>, &mut Vec<(<T2::Cursor as Cursor>::ValOwned, T2::Diff)>)+'static,
     {
         self.arrange_by_key_named(&format!("Arrange: {}", name))
@@ -310,7 +310,7 @@ where
     T2: for<'a> Trace<Key<'a>=T1::Key<'a>, Time=T1::Time> + 'static,
     T2::ValOwned: Data,
     T2::Batch: Batch,
-    T2::Builder: Builder<Output=T2::Batch, Item = ((T1::KeyOwned, T2::ValOwned), T2::Time, T2::Diff)>,
+    T2::Builder: Builder<Input = ((T1::KeyOwned, T2::ValOwned), T2::Time, T2::Diff)>,
     L: FnMut(T1::Key<'_>, &[(T1::Val<'_>, T1::Diff)], &mut Vec<(T2::ValOwned,T2::Diff)>, &mut Vec<(T2::ValOwned, T2::Diff)>)+'static,
 {
     let mut result_trace = None;
diff --git a/src/trace/implementations/merge_batcher.rs b/src/trace/implementations/merge_batcher.rs
index 673fedce6..2cf27ed1b 100644
--- a/src/trace/implementations/merge_batcher.rs
+++ b/src/trace/implementations/merge_batcher.rs
@@ -25,8 +25,8 @@ where
     T: Timestamp,
     D: Semigroup,
 {
-    type Input = Vec<Self::Item>;
-    type Item = ((K,V),T,D);
+    type Input = Vec<((K,V),T,D)>;
+    type Output = ((K,V),T,D);
     type Time = T;
 
     fn new(logger: Option<Logger<DifferentialEvent, WorkerIdentifier>>, operator_id: usize) -> Self {
@@ -38,7 +38,7 @@ where
     }
 
     #[inline(never)]
-    fn push_batch(&mut self, batch: RefOrMut<Vec<Self::Item>>) {
+    fn push_batch(&mut self, batch: RefOrMut<Self::Input>) {
         // `batch` is either a shared reference or an owned allocations.
         match batch {
             RefOrMut::Ref(reference) => {
@@ -59,7 +59,7 @@ where
     // which we call `lower`, by assumption that after sealing a batcher we receive no more
     // updates with times not greater or equal to `upper`.
     #[inline(never)]
-    fn seal<B: Builder<Item=Self::Item, Time=Self::Time>>(&mut self, upper: Antichain<T>) -> B::Output {
+    fn seal<B: Builder<Input=Self::Output, Time=Self::Time>>(&mut self, upper: Antichain<T>) -> B::Output {
 
         let mut merged = Vec::new();
         self.sorter.finish_into(&mut merged);
diff --git a/src/trace/implementations/merge_batcher_col.rs b/src/trace/implementations/merge_batcher_col.rs
index 7989eece8..21416170d 100644
--- a/src/trace/implementations/merge_batcher_col.rs
+++ b/src/trace/implementations/merge_batcher_col.rs
@@ -31,8 +31,8 @@ where
     T: Columnation + Timestamp + 'static,
     D: Columnation + Semigroup + 'static,
 {
-    type Input = Vec<Self::Item>;
-    type Item = ((K,V),T,D);
+    type Input = Vec<((K,V),T,D)>;
+    type Output = ((K,V),T,D);
     type Time = T;
 
     fn new(logger: Option<Logger<DifferentialEvent, WorkerIdentifier>>, operator_id: usize) -> Self {
@@ -44,7 +44,7 @@ where
     }
 
     #[inline]
-    fn push_batch(&mut self, batch: RefOrMut<Vec<Self::Item>>) {
+    fn push_batch(&mut self, batch: RefOrMut<Self::Input>) {
         // `batch` is either a shared reference or an owned allocations.
         match batch {
             RefOrMut::Ref(reference) => {
@@ -63,7 +63,7 @@ where
     // which we call `lower`, by assumption that after sealing a batcher we receive no more
     // updates with times not greater or equal to `upper`.
     #[inline]
-    fn seal<B: Builder<Item=Self::Item, Time=Self::Time>>(&mut self, upper: Antichain<T>) -> B::Output {
+    fn seal<B: Builder<Input=Self::Output, Time=Self::Time>>(&mut self, upper: Antichain<T>) -> B::Output {
 
         let mut merged = Default::default();
         self.sorter.finish_into(&mut merged);
diff --git a/src/trace/implementations/ord_neu.rs b/src/trace/implementations/ord_neu.rs
index bf4dd9544..ce0c6532a 100644
--- a/src/trace/implementations/ord_neu.rs
+++ b/src/trace/implementations/ord_neu.rs
@@ -540,7 +540,7 @@ mod val_batch {
 
     impl<L: Layout> Builder for OrdValBuilder<L> {
 
-        type Item = ((<L::Target as Update>::Key, <L::Target as Update>::Val), <L::Target as Update>::Time, <L::Target as Update>::Diff);
+        type Input = ((<L::Target as Update>::Key, <L::Target as Update>::Val), <L::Target as Update>::Time, <L::Target as Update>::Diff);
         type Time = <L::Target as Update>::Time;
         type Output = OrdValBatch<L>;
 
@@ -560,7 +560,7 @@ mod val_batch {
         }
 
         #[inline]
-        fn push(&mut self, ((key, val), time, diff): Self::Item) {
+        fn push(&mut self, ((key, val), time, diff): Self::Input) {
 
             // Perhaps this is a continuation of an already received key.
             if self.result.keys.last().map(|k| k.equals(&key)).unwrap_or(false) {
@@ -586,7 +586,7 @@ mod val_batch {
         }
 
         #[inline]
-        fn copy(&mut self, ((key, val), time, diff): &Self::Item) {
+        fn copy(&mut self, ((key, val), time, diff): &Self::Input) {
 
             // Perhaps this is a continuation of an already received key.
             if self.result.keys.last().map(|k| k.equals(key)).unwrap_or(false) {
@@ -1006,7 +1006,7 @@ mod key_batch {
 
     impl<L: Layout> Builder for OrdKeyBuilder<L> {
 
-        type Item = ((<L::Target as Update>::Key, ()), <L::Target as Update>::Time, <L::Target as Update>::Diff);
+        type Input = ((<L::Target as Update>::Key, ()), <L::Target as Update>::Time, <L::Target as Update>::Diff);
         type Time = <L::Target as Update>::Time;
         type Output = OrdKeyBatch<L>;
 
@@ -1024,7 +1024,7 @@ mod key_batch {
         }
 
         #[inline]
-        fn push(&mut self, ((key, ()), time, diff): Self::Item) {
+        fn push(&mut self, ((key, ()), time, diff): Self::Input) {
 
             // Perhaps this is a continuation of an already received key.
             if self.result.keys.last().map(|k| k.equals(&key)).unwrap_or(false) {
@@ -1040,7 +1040,7 @@ mod key_batch {
         }
 
         #[inline]
-        fn copy(&mut self, ((key, ()), time, diff): &Self::Item) {
+        fn copy(&mut self, ((key, ()), time, diff): &Self::Input) {
 
             // Perhaps this is a continuation of an already received key.
             if self.result.keys.last().map(|k| k.equals(key)).unwrap_or(false) {
diff --git a/src/trace/implementations/rhh.rs b/src/trace/implementations/rhh.rs
index 94ed3b95b..f29d39a8b 100644
--- a/src/trace/implementations/rhh.rs
+++ b/src/trace/implementations/rhh.rs
@@ -731,7 +731,7 @@ mod val_batch {
         <L::Target as Update>::Key: Default + HashOrdered,
         // RhhValBatch<L>: Batch<Key=<L::Target as Update>::Key, Val=<L::Target as Update>::Val, Time=<L::Target as Update>::Time, Diff=<L::Target as Update>::Diff>,
     {
-        type Item = ((<L::Target as Update>::Key, <L::Target as Update>::Val), <L::Target as Update>::Time, <L::Target as Update>::Diff);
+        type Input = ((<L::Target as Update>::Key, <L::Target as Update>::Val), <L::Target as Update>::Time, <L::Target as Update>::Diff);
         type Time = <L::Target as Update>::Time;
         type Output = RhhValBatch<L>;
 
@@ -763,7 +763,7 @@ mod val_batch {
         }
 
         #[inline]
-        fn push(&mut self, ((key, val), time, diff): Self::Item) {
+        fn push(&mut self, ((key, val), time, diff): Self::Input) {
 
             // Perhaps this is a continuation of an already received key.
             if self.result.keys.last().map(|k| k.equals(&key)).unwrap_or(false) {
@@ -790,7 +790,7 @@ mod val_batch {
         }
 
         #[inline]
-        fn copy(&mut self, ((key, val), time, diff): &Self::Item) {
+        fn copy(&mut self, ((key, val), time, diff): &Self::Input) {
 
             // Perhaps this is a continuation of an already received key.
             if self.result.keys.last().map(|k| k.equals(key)).unwrap_or(false) {
diff --git a/src/trace/implementations/spine_fueled.rs b/src/trace/implementations/spine_fueled.rs
index fd3af3b76..c616e2b7d 100644
--- a/src/trace/implementations/spine_fueled.rs
+++ b/src/trace/implementations/spine_fueled.rs
@@ -255,7 +255,7 @@ impl<B, BA, BU> Trace for Spine<B, BA, BU>
 where
     B: Batch+Clone+'static,
     BA: Batcher<Time = B::Time>,
-    BU: Builder<Item=BA::Item, Time=BA::Time, Output = B>,
+    BU: Builder<Input=BA::Output, Time=BA::Time, Output = B>,
 {
     /// A type used to assemble batches from disordered updates.
     type Batcher = BA;
diff --git a/src/trace/mod.rs b/src/trace/mod.rs
index d0d6791e3..145c2990f 100644
--- a/src/trace/mod.rs
+++ b/src/trace/mod.rs
@@ -213,7 +213,7 @@ where <Self as TraceReader>::Batch: Batch {
     /// A type used to assemble batches from disordered updates.
     type Batcher: Batcher<Time = Self::Time>;
     /// A type used to assemble batches from ordered update sequences.
-    type Builder: Builder<Item=<Self::Batcher as Batcher>::Item, Time=Self::Time, Output = Self::Batch>;
+    type Builder: Builder<Input=<Self::Batcher as Batcher>::Output, Time=Self::Time, Output = Self::Batch>;
 
     /// Allocates a new empty trace.
     fn new(
@@ -306,10 +306,10 @@ pub trait Batch : BatchReader where Self: ::std::marker::Sized {
 
 /// Functionality for collecting and batching updates.
 pub trait Batcher {
-    /// Type of update pushed into the batcher.
+    /// Type pushed into the batcher.
     type Input;
-    /// Type of update pushed into the builder.
-    type Item;
+    /// Type produced by the batcher.
+    type Output;
     /// Times at which batches are formed.
     type Time: Timestamp;
     /// Allocates a new empty batcher.
@@ -317,7 +317,7 @@ pub trait Batcher {
     /// Adds an unordered batch of elements to the batcher.
     fn push_batch(&mut self, batch: RefOrMut<Self::Input>);
     /// Returns all updates not greater or equal to an element of `upper`.
-    fn seal<B: Builder<Item=Self::Item, Time=Self::Time>>(&mut self, upper: Antichain<Self::Time>) -> B::Output;
+    fn seal<B: Builder<Input=Self::Output, Time=Self::Time>>(&mut self, upper: Antichain<Self::Time>) -> B::Output;
     /// Returns the lower envelope of contained update times.
     fn frontier(&mut self) -> timely::progress::frontier::AntichainRef<Self::Time>;
 }
@@ -325,7 +325,7 @@ pub trait Batcher {
 /// Functionality for building batches from ordered update sequences.
 pub trait Builder: Sized {
     /// Input item type.
-    type Item;
+    type Input;
     /// Timestamp type.
     type Time: Timestamp;
     /// Output batch type.
@@ -344,15 +344,11 @@ pub trait Builder: Sized {
     ///
     /// The default implementation uses `self.copy` with references to the owned arguments.
     /// One should override it if the builder can take advantage of owned arguments.
-    fn push(&mut self, element: Self::Item) {
+    fn push(&mut self, element: Self::Input) {
         self.copy(&element);
     }
     /// Adds an element to the batch.
-    fn copy(&mut self, element: &Self::Item);
-    /// Adds an ordered sequence of elements to the batch.
-    fn extend<I: Iterator<Item=Self::Item>>(&mut self, iter: I) {
-        for item in iter { self.push(item); }
-    }
+    fn copy(&mut self, element: &Self::Input);
     /// Completes building and returns the batch.
     fn done(self, lower: Antichain<Self::Time>, upper: Antichain<Self::Time>, since: Antichain<Self::Time>) -> Self::Output;
 }
@@ -460,12 +456,12 @@ pub mod rc_blanket_impls {
 
     /// Functionality for building batches from ordered update sequences.
     impl<B: Builder> Builder for RcBuilder<B> {
-        type Item = B::Item;
+        type Input = B::Input;
         type Time = B::Time;
         type Output = Rc<B::Output>;
         fn with_capacity(keys: usize, vals: usize, upds: usize) -> Self { RcBuilder { builder: B::with_capacity(keys, vals, upds) } }
-        fn push(&mut self, element: Self::Item) { self.builder.push(element) }
-        fn copy(&mut self, element: &Self::Item) { self.builder.copy(element) }
+        fn push(&mut self, element: Self::Input) { self.builder.push(element) }
+        fn copy(&mut self, element: &Self::Input) { self.builder.copy(element) }
         fn done(self, lower: Antichain<Self::Time>, upper: Antichain<Self::Time>, since: Antichain<Self::Time>) -> Rc<B::Output> { Rc::new(self.builder.done(lower, upper, since)) }
     }
 
@@ -569,12 +565,12 @@ pub mod abomonated_blanket_impls {
     where
         B::Output: Abomonation,
     {
-        type Item = B::Item;
+        type Input = B::Input;
         type Time = B::Time;
         type Output = Abomonated<B::Output, Vec<u8>>;
         fn with_capacity(keys: usize, vals: usize, upds: usize) -> Self { AbomonatedBuilder { builder: B::with_capacity(keys, vals, upds) } }
-        fn push(&mut self, element: Self::Item) { self.builder.push(element) }
-        fn copy(&mut self, element: &Self::Item) { self.builder.copy(element) }
+        fn push(&mut self, element: Self::Input) { self.builder.push(element) }
+        fn copy(&mut self, element: &Self::Input) { self.builder.copy(element) }
         fn done(self, lower: Antichain<Self::Time>, upper: Antichain<Self::Time>, since: Antichain<Self::Time>) -> Self::Output {
             let batch = self.builder.done(lower, upper, since);
             let mut bytes = Vec::with_capacity(measure(&batch));