diff --git a/differential-dataflow/src/operators/arrange/upsert.rs b/differential-dataflow/src/operators/arrange/upsert.rs
index 725321edf..fa556327d 100644
--- a/differential-dataflow/src/operators/arrange/upsert.rs
+++ b/differential-dataflow/src/operators/arrange/upsert.rs
@@ -98,7 +98,7 @@
 //! }).unwrap();
 //! ```
 
-use std::collections::{BinaryHeap, HashMap};
+use std::collections::{BinaryHeap, BTreeMap};
 
 use timely::order::{PartialOrder, TotalOrder};
 use timely::dataflow::{Scope, Stream};
@@ -216,7 +216,7 @@ where
                                 }
 
                                 // Extract upserts available to process as of this `upper`.
-                                let mut to_process = HashMap::new();
+                                let mut to_process = BTreeMap::new();
                                 while priority_queue.peek().map(|std::cmp::Reverse((t,_k,_v))| !upper.less_equal(t)).unwrap_or(false) {
                                     let std::cmp::Reverse((time, key, val)) = priority_queue.pop().expect("Priority queue just ensured non-empty");
                                     to_process.entry(key).or_insert(Vec::new()).push((time, std::cmp::Reverse(val)));
@@ -229,15 +229,11 @@ where
                                     priority_queue.shrink_to_fit();
                                 }
 
-                                // Put (key, list) into key order, to match cursor enumeration.
-                                let mut to_process = to_process.into_iter().collect::<Vec<_>>();
-                                to_process.sort();
-
                                 // Prepare a cursor to the existing arrangement, and a batch builder for
                                 // new stuff that we add.
                                 let (mut trace_cursor, trace_storage) = reader_local.cursor();
                                 let mut builder = Bu::new();
-                                for (key, mut list) in to_process.drain(..) {
+                                for (key, mut list) in to_process {
 
                                     // The prior value associated with the key.
                                     let mut prev_value: Option<V> = None;