diff --git a/src/operator/distinct.rs b/src/operator/distinct.rs
index e4640825..72d5ac3a 100644
--- a/src/operator/distinct.rs
+++ b/src/operator/distinct.rs
@@ -9,17 +9,16 @@ use crate::{
     },
     circuit_cache_key,
     time::NestedTimestamp32,
-    trace::{ord::OrdKeySpine, BatchReader, Builder, Cursor as TraceCursor, Trace, TraceReader},
+    trace::{ord::OrdKeySpine, BatchReader, Builder, Cursor as TraceCursor, Trace},
     NumEntries, Timestamp,
 };
 use size_of::SizeOf;
 use std::{
     borrow::Cow,
-    cmp::{max, Ordering},
-    collections::BTreeSet,
+    cmp::Ordering,
+    collections::{BTreeSet, HashMap},
     hash::Hash,
     marker::PhantomData,
-    mem::take,
     ops::{Add, Neg},
 };
 
@@ -299,12 +298,12 @@ where
 pub struct DistinctTrace<Z, T>
 where
     Z: ZSet,
-    T: TraceReader<Key = Z::Key, Val = (), R = Z::R> + 'static,
+    T: BatchReader<Key = Z::Key, Val = (), R = Z::R> + 'static,
 {
     // Keeps track of keys that need to be considered at future times.
     // Specifically, `future_updates[i]` accumulates all keys observed during
     // the current epoch whose weight can change at time `i`.
-    future_updates: Vec<BTreeSet<Z::Key>>,
+    future_updates: HashMap<u32, BTreeSet<Z::Key>>,
     // TODO: not needed once timekeeping is handled by the circuit.
     time: u32,
     empty_input: bool,
@@ -315,12 +314,12 @@ where
 impl<Z, T> DistinctTrace<Z, T>
 where
     Z: ZSet,
-    T: TraceReader<Key = Z::Key, Val = (), R = Z::R> + 'static,
+    T: BatchReader<Key = Z::Key, Val = (), R = Z::R> + 'static,
     T::Time: Timestamp,
 {
     fn new() -> Self {
         Self {
-            future_updates: Vec::new(),
+            future_updates: HashMap::new(),
             time: HasZero::zero(),
             empty_input: false,
             empty_output: false,
@@ -334,7 +333,7 @@ where
     Z: ZSet,
     Z::Key: Clone + Ord + PartialEq,
     Z::R: ZRingValue,
-    T: TraceReader<Key = Z::Key, Val = (), Time = NestedTimestamp32, R = Z::R> + 'static,
+    T: BatchReader<Key = Z::Key, Val = (), Time = NestedTimestamp32, R = Z::R> + 'static,
 {
     // Evaluate nested incremental distinct for a single value.
     //
@@ -446,7 +445,10 @@ where
             // Record next_ts in `self.future_updates`.
             if let Some(next_ts) = next_ts {
                 let idx: usize = next_ts.inner() as usize;
-                self.future_updates[idx].insert(value.clone());
+                self.future_updates
+                    .entry(idx as u32)
+                    .or_insert_with(BTreeSet::new)
+                    .insert(value.clone());
             }
         } else if weight.ge0() && !weight.is_zero() {
             builder.push((Z::item_from(value.clone(), ()), HasOne::one()));
@@ -458,14 +460,14 @@ impl<Z, T> Operator for DistinctTrace<Z, T>
 where
     Z: ZSet,
     Z::Key: SizeOf + Clone + Ord + PartialEq,
-    T: TraceReader<Key = Z::Key, Val = (), Time = NestedTimestamp32, R = Z::R> + 'static,
+    T: BatchReader<Key = Z::Key, Val = (), Time = NestedTimestamp32, R = Z::R> + 'static,
 {
     fn name(&self) -> Cow<'static, str> {
         Cow::Borrowed("DistinctTrace")
     }
 
     fn metadata(&self, meta: &mut OperatorMeta) {
-        let size: usize = self.future_updates.iter().map(BTreeSet::len).sum();
+        let size: usize = self.future_updates.values().map(BTreeSet::len).sum();
         let bytes = self.future_updates.size_of();
 
         meta.extend(metadata! {
@@ -495,11 +497,7 @@ where
         assert_eq!(scope, 0);
         self.empty_input
             && self.empty_output
-            && self
-                .future_updates
-                .iter()
-                .skip(self.time as usize)
-                .all(|vals| vals.is_empty())
+            && self.future_updates.values().all(|vals| vals.is_empty())
     }
 }
 
@@ -527,7 +525,7 @@ where
     //   appeared in one of the previous epochs at time `t`.
     //
     // To efficiently compute keys that satisfy the second condition, we use the
-    // `future_updates` vector, where for each key observed in the current epoch
+    // `future_updates` map, where for each key observed in the current epoch
     // at time `t1` we lookup the smallest time `t2 > t1` (if any) at which we saw
     // the key during any previous epochs and record this key in
     // `future_updates[t2]`. Then when evaluating an operatpr at time `t` we
@@ -541,26 +539,13 @@ where
 
         self.empty_input = delta.is_zero();
 
-        // Make sure we have enough room in `future_updates` to
-        // accommodate the largest timestamp in the trace, so we don't
-        // need to worry about growing `future_updates` later on.
-        let mut new_len: u32 = self.time + 1;
-        trace.map_batches(|batch| {
-            for ts in batch.upper() {
-                new_len = max(new_len, ts.inner() + 1);
-            }
-        });
-
-        self.future_updates
-            .resize(new_len as usize, BTreeSet::new());
-
         let mut builder = Z::Builder::with_capacity((), delta.len());
 
         let mut trace_cursor = trace.cursor();
 
         // For all keys in delta, for all keys in future_updates[time].
         let mut delta_cursor = delta.cursor();
-        let candidates = take(&mut self.future_updates[self.time as usize]);
+        let candidates = self.future_updates.remove(&self.time).unwrap_or_default();
         let mut cand_iterator = candidates.iter();
 
         let mut candidate = cand_iterator.next();
diff --git a/src/operator/join.rs b/src/operator/join.rs
index 4f63a870..1f4986e3 100644
--- a/src/operator/join.rs
+++ b/src/operator/join.rs
@@ -10,7 +10,7 @@ use crate::{
     time::Timestamp,
     trace::{
         cursor::Cursor as TraceCursor, spine_fueled::Spine, Batch, BatchReader, Batcher, Builder,
-        Trace, TraceReader,
+        Trace,
     },
     OrdIndexedZSet, OrdZSet,
 };
@@ -549,7 +549,7 @@ impl JoinStats {
 
 pub struct JoinTrace<F, I, T, Z, It>
 where
-    T: TraceReader,
+    T: BatchReader,
     Z: IndexedZSet,
 {
     join_func: F,
@@ -569,7 +569,7 @@ where
 
 impl<F, I, T, Z, It> JoinTrace<F, I, T, Z, It>
 where
-    T: TraceReader,
+    T: BatchReader,
     Z: IndexedZSet,
 {
     pub fn new(join_func: F, location: &'static Location<'static>) -> Self {
@@ -590,7 +590,7 @@ impl<F, I, T, Z, It> Operator for JoinTrace<F, I, T, Z, It>
 where
     F: 'static,
     I: 'static,
-    T: TraceReader + 'static,
+    T: BatchReader + 'static,
     Z: IndexedZSet,
     Z::Batcher: SizeOf,
     It: 'static,
diff --git a/src/operator/trace.rs b/src/operator/trace.rs
index 42131cc6..b9aaa599 100644
--- a/src/operator/trace.rs
+++ b/src/operator/trace.rs
@@ -5,7 +5,7 @@ use crate::{
         Circuit, ExportId, ExportStream, GlobalNodeId, OwnershipPreference, Scope, Stream,
     },
     circuit_cache_key,
-    trace::{cursor::Cursor, spine_fueled::Spine, Batch, BatchReader, Builder, Trace, TraceReader},
+    trace::{cursor::Cursor, spine_fueled::Spine, Batch, BatchReader, Builder, Trace},
     NumEntries, Timestamp,
 };
 use size_of::SizeOf;
@@ -154,7 +154,7 @@ where
 impl<P, T> Stream<Circuit<P>, T>
 where
     P: Clone + 'static,
-    T: TraceReader + 'static,
+    T: Trace + 'static,
 {
     pub fn delay_trace(&self) -> Stream<Circuit<P>, T> {
         self.circuit()
@@ -168,14 +168,14 @@ where
 
 pub struct UntimedTraceAppend<T>
 where
-    T: TraceReader,
+    T: Trace,
 {
     _phantom: PhantomData<T>,
 }
 
 impl<T> UntimedTraceAppend<T>
 where
-    T: TraceReader,
+    T: Trace,
 {
     pub fn new() -> Self {
         Self {
@@ -186,7 +186,7 @@ where
 
 impl<T> Default for UntimedTraceAppend<T>
 where
-    T: TraceReader,
+    T: Trace,
 {
     fn default() -> Self {
         Self::new()
@@ -195,7 +195,7 @@ where
 
 impl<T> Operator for UntimedTraceAppend<T>
 where
-    T: TraceReader + 'static,
+    T: Trace + 'static,
 {
     fn name(&self) -> Cow<'static, str> {
         Cow::from("UntimedTraceAppend")
@@ -241,7 +241,7 @@ where
 
 pub struct TraceAppend<T, B>
 where
-    T: TraceReader,
+    T: Trace,
 {
     time: T::Time,
     _phantom: PhantomData<B>,
@@ -249,7 +249,7 @@ where
 
 impl<T, B> TraceAppend<T, B>
 where
-    T: TraceReader,
+    T: Trace,
 {
     pub fn new() -> Self {
         Self {
@@ -261,7 +261,7 @@ where
 
 impl<T, B> Default for TraceAppend<T, B>
 where
-    T: TraceReader,
+    T: Trace,
 {
     fn default() -> Self {
         Self::new()
@@ -270,7 +270,7 @@ where
 
 impl<T, B> Operator for TraceAppend<T, B>
 where
-    T: TraceReader + 'static,
+    T: Trace + 'static,
     B: 'static,
 {
     fn name(&self) -> Cow<'static, str> {
@@ -325,7 +325,7 @@ where
     }
 }
 
-pub struct Z1Trace<T: TraceReader> {
+pub struct Z1Trace<T: Trace> {
     time: T::Time,
     trace: Option<T>,
     // `dirty[scope]` is `true` iff at least one non-empty update was added to the trace
diff --git a/src/operator/upsert.rs b/src/operator/upsert.rs
index 6480462d..643728aa 100644
--- a/src/operator/upsert.rs
+++ b/src/operator/upsert.rs
@@ -6,8 +6,8 @@ use crate::{
     },
     operator::trace::{DelayedTraceId, TraceAppend, TraceId, Z1Trace},
     trace::{
-        consolidation::consolidate, cursor::Cursor, spine_fueled::Spine, Batch, Builder, Trace,
-        TraceReader,
+        consolidation::consolidate, cursor::Cursor, spine_fueled::Spine, Batch, BatchReader,
+        Builder, Trace,
     },
     utils::VecExt,
     Circuit, Stream, Timestamp,
@@ -98,7 +98,7 @@ where
 
 pub struct Upsert<T, B>
 where
-    T: TraceReader,
+    T: BatchReader,
 {
     time: T::Time,
     phantom: PhantomData<B>,
@@ -106,7 +106,7 @@ where
 
 impl<T, B> Upsert<T, B>
 where
-    T: TraceReader,
+    T: BatchReader,
 {
     pub fn new() -> Self {
         Self {
@@ -118,7 +118,7 @@ where
 
 impl<T, B> Default for Upsert<T, B>
 where
-    T: TraceReader,
+    T: BatchReader,
 {
     fn default() -> Self {
         Self::new()
@@ -127,7 +127,7 @@ where
 
 impl<T, B> Operator for Upsert<T, B>
 where
-    T: TraceReader + 'static,
+    T: BatchReader + 'static,
     B: 'static,
 {
     fn name(&self) -> Cow<'static, str> {
diff --git a/src/trace/mod.rs b/src/trace/mod.rs
index e99c7e4c..1af4702e 100644
--- a/src/trace/mod.rs
+++ b/src/trace/mod.rs
@@ -25,40 +25,14 @@ use crate::{
 };
 use size_of::SizeOf;
 
-/// A trace whose contents may be read.
-///
-/// This is a restricted interface to the more general `Trace` trait, which
-/// extends this trait with further methods to update the contents of the trace.
-/// These methods are used to examine the contents, and to update the reader's
-/// capabilities (which may release restrictions on the mutations to the
-/// underlying trace and cause work to happen).
-pub trait TraceReader: BatchReader {
-    /// The type of an immutable collection of updates.
-    type Batch: Batch<Key = Self::Key, Val = Self::Val, Time = Self::Time, R = Self::R> + 'static;
-
-    // TODO: Do we want a version of `cursor` with an upper bound on time?  E.g., it
-    // could help in `distinct` to avoid iterating into the future (and then
-    // drop future timestamps anyway).
-    /*
-    /// Acquires a cursor to the restriction of the collection's contents to updates at times not greater or
-    /// equal to an element of `upper`.
-    ///
-    /// This method is expected to work if called with an `upper` that (i) was an observed bound in batches from
-    /// the trace, and (ii) the trace has not been advanced beyond `upper`. Practically, the implementation should
-    /// be expected to look for a "clean cut" using `upper`, and if it finds such a cut can return a cursor. This
-    /// should allow `upper` such as `&[]` as used by `self.cursor()`, though it is difficult to imagine other uses.
-    fn cursor_through(&self, upper: AntichainRef<Self::Time>) -> Option<(Self::Cursor, <Self::Cursor as Cursor<Self::Key, Self::Val, Self::Time, Self::R>>::Storage)>;
-    */
-
-    /// Maps logic across the non-empty sequence of batches in the trace.
-    fn map_batches<F: FnMut(&Self::Batch)>(&self, f: F);
-}
-
 /// An append-only collection of `(key, val, time, diff)` tuples.
 ///
 /// The trace must be constructable from, and navigable by the `Key`, `Val`,
 /// `Time` types, but does not need to return them.
-pub trait Trace: TraceReader {
+pub trait Trace: BatchReader {
+    /// The type of an immutable collection of updates.
+    type Batch: Batch<Key = Self::Key, Val = Self::Val, Time = Self::Time, R = Self::R> + 'static;
+
     /// Allocates a new empty trace.
     fn new(activator: Option<Activator>) -> Self;
 
diff --git a/src/trace/spine_fueled.rs b/src/trace/spine_fueled.rs
index f5bf806c..80144e57 100644
--- a/src/trace/spine_fueled.rs
+++ b/src/trace/spine_fueled.rs
@@ -85,7 +85,7 @@ use crate::{
     trace::{
         cursor::{Cursor, CursorList},
         rc_blanket_impls::RcBatchCursor,
-        Batch, BatchReader, Consumer, Merger, Trace, TraceReader, ValueConsumer,
+        Batch, BatchReader, Consumer, Merger, Trace, ValueConsumer,
     },
     NumEntries,
 };
@@ -238,15 +238,11 @@ where
     }
 }
 
-impl<B> TraceReader for Spine<B>
+impl<B> Spine<B>
 where
     B: Batch + 'static,
-    B::Key: Ord,
-    B::Val: Ord,
 {
-    type Batch = B;
-
-    fn map_batches<F: FnMut(&Self::Batch)>(&self, mut f: F) {
+    fn map_batches<F: FnMut(&B)>(&self, mut f: F) {
         for batch in self.merging.iter().rev() {
             match batch {
                 MergeState::Double(MergeVariant::InProgress(batch1, batch2, _)) => {
@@ -438,6 +434,8 @@ where
     B::Key: Ord,
     B::Val: Ord,
 {
+    type Batch = B;
+
     fn new(activator: Option<Activator>) -> Self {
         Self::with_effort(1, activator)
     }
@@ -476,7 +474,7 @@ where
         }
     }
 
-    fn consolidate(mut self) -> Option<Self::Batch> {
+    fn consolidate(mut self) -> Option<B> {
         // Merge batches until there is nothing left to merge.
         let mut fuel = isize::max_value();
         while !self.reduced() {
@@ -865,7 +863,7 @@ where
 
     /// Mutate all batches.  Can only be invoked when there are no in-progress
     /// matches in the trait.
-    fn map_batches_mut<F: FnMut(&mut <Self as TraceReader>::Batch)>(&mut self, mut f: F) {
+    fn map_batches_mut<F: FnMut(&mut <Self as Trace>::Batch)>(&mut self, mut f: F) {
         for batch in self.merging.iter_mut().rev() {
             match batch {
                 MergeState::Double(MergeVariant::InProgress(_batch1, _batch2, _)) => {