diff --git a/src/gadgets/sorting.rs b/src/gadgets/sorting.rs
index 21601988..5f074f94 100644
--- a/src/gadgets/sorting.rs
+++ b/src/gadgets/sorting.rs
@@ -1,13 +1,21 @@
 use itertools::izip;
 
 use crate::field::extension_field::Extendable;
-use crate::field::field_types::RichField;
+use crate::field::field_types::{Field, RichField};
 use crate::gates::comparison::ComparisonGate;
 use crate::iop::generator::{GeneratedValues, SimpleGenerator};
 use crate::iop::target::{BoolTarget, Target};
 use crate::iop::witness::{PartitionWitness, Witness};
 use crate::plonk::circuit_builder::CircuitBuilder;
 use crate::util::ceil_div_usize;
+use std::marker::PhantomData;
+
+pub struct MemoryOp<F: Field> {
+    is_write: bool,
+    address: F,
+    timestamp: F,
+    value: F,
+}
 
 #[derive(Clone, Debug)]
 pub struct MemoryOpTarget {
@@ -39,14 +47,12 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         rhs: Target,
         bits: usize,
         num_chunks: usize,
-    ) -> (ComparisonGate<F, D>, usize) {
+    ) {
         let gate = ComparisonGate::new(bits, num_chunks);
         let gate_index = self.add_gate(gate.clone(), vec![]);
 
         self.connect(Target::wire(gate_index, gate.wire_first_input()), lhs);
         self.connect(Target::wire(gate_index, gate.wire_second_input()), rhs);
-
-        (gate, gate_index)
     }
 
     /// Sort memory operations by address value, then by timestamp value.
@@ -94,29 +100,21 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
             .map(|op| self.mul_add(op.address, two_n, op.timestamp))
             .collect();
 
-        let mut gates = Vec::new();
-        let mut gate_indices = Vec::new();
         for i in 1..n {
-            let (gate, gate_index) = self.assert_le(
+            self.assert_le(
                 address_timestamp_combined[i - 1],
                 address_timestamp_combined[i],
                 combined_bits,
                 num_chunks,
             );
-
-            gate_indices.push(gate_index);
-            gates.push(gate);
         }
 
-        self.assert_permutation_memory_ops(ops, output_targets.as_slice());
+        self.assert_permutation_memory_ops(ops, &output_targets);
 
         self.add_simple_generator(MemoryOpSortGenerator::<F, D> {
             input_ops: ops.to_vec(),
-            gate_indices,
-            gates: gates.clone(),
             output_ops: output_targets.clone(),
-            address_bits,
-            timestamp_bits,
+            _phantom: PhantomData,
         });
 
         output_targets
@@ -126,11 +124,8 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
 #[derive(Debug)]
 struct MemoryOpSortGenerator<F: RichField + Extendable<D>, const D: usize> {
     input_ops: Vec<MemoryOpTarget>,
-    gate_indices: Vec<usize>,
-    gates: Vec<ComparisonGate<F, D>>,
     output_ops: Vec<MemoryOpTarget>,
-    address_bits: usize,
-    timestamp_bits: usize,
+    _phantom: PhantomData<F::Extension>,
 }
 
 impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F>
@@ -148,61 +143,43 @@ impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F>
         let n = self.input_ops.len();
         debug_assert!(self.output_ops.len() == n);
 
-        let (timestamp_values, address_values): (Vec<_>, Vec<_>) = self
+        let mut ops: Vec<_> = self
             .input_ops
             .iter()
             .map(|op| {
-                (
-                    witness.get_target(op.timestamp),
-                    witness.get_target(op.address),
-                )
-            })
-            .unzip();
-
-        let combined_values: Vec<_> = timestamp_values
-            .iter()
-            .zip(&address_values)
-            .map(|(&t, &a)| {
-                F::from_canonical_u64(
-                    (a.to_canonical_u64() << self.timestamp_bits as u64) + t.to_canonical_u64(),
-                )
+                let is_write = witness.get_bool_target(op.is_write);
+                let address = witness.get_target(op.address);
+                let timestamp = witness.get_target(op.timestamp);
+                let value = witness.get_target(op.value);
+                MemoryOp {
+                    is_write,
+                    address,
+                    timestamp,
+                    value,
+                }
             })
             .collect();
 
-        let mut input_ops_and_keys: Vec<_> = self
-            .input_ops
-            .iter()
-            .zip(combined_values)
-            .collect::<Vec<_>>();
-        input_ops_and_keys.sort_by_key(|(_, val)| val.to_canonical_u64());
+        ops.sort_unstable_by_key(|op| {
+            (
+                op.address.to_canonical_u64(),
+                op.timestamp.to_canonical_u64(),
+            )
+        });
 
-        for i in 0..n {
-            out_buffer.set_target(
-                self.output_ops[i].is_write.target,
-                witness.get_target(input_ops_and_keys[i].0.is_write.target),
-            );
-            out_buffer.set_target(
-                self.output_ops[i].address,
-                witness.get_target(input_ops_and_keys[i].0.address),
-            );
-            out_buffer.set_target(
-                self.output_ops[i].timestamp,
-                witness.get_target(input_ops_and_keys[i].0.timestamp),
-            );
-            out_buffer.set_target(
-                self.output_ops[i].value,
-                witness.get_target(input_ops_and_keys[i].0.value),
-            );
+        for (op, out_op) in ops.iter().zip(&self.output_ops) {
+            out_buffer.set_target(out_op.is_write.target, F::from_bool(op.is_write));
+            out_buffer.set_target(out_op.address, op.address);
+            out_buffer.set_target(out_op.timestamp, op.timestamp);
+            out_buffer.set_target(out_op.value, op.value);
         }
     }
 }
 
 #[cfg(test)]
 mod tests {
-    use std::collections::HashSet;
-
     use anyhow::Result;
-    use rand::{seq::SliceRandom, thread_rng, Rng};
+    use rand::{thread_rng, Rng};
 
     use super::*;
     use crate::field::crandall_field::CrandallField;