diff --git a/evm/src/cpu/columns.rs b/evm/src/cpu/columns.rs
index 51e47abb..31e25884 100644
--- a/evm/src/cpu/columns.rs
+++ b/evm/src/cpu/columns.rs
@@ -163,6 +163,7 @@ pub(crate) const NUM_MEMORY_VALUE_LIMBS: usize = 8;
 
 pub(crate) const CLOCK: usize = SIMPLE_LOGIC_DIFF_INV + 1;
 
+// Uses_memop(i) is `F::ONE` iff this row includes a memory operation in its `i`th spot.
 const USES_MEMOP_START: usize = CLOCK + 1;
 pub const fn uses_memop(op: usize) -> usize {
     debug_assert!(op < NUM_MEMORY_OPS);
diff --git a/evm/src/lib.rs b/evm/src/lib.rs
index f60ea23c..422fae29 100644
--- a/evm/src/lib.rs
+++ b/evm/src/lib.rs
@@ -3,7 +3,6 @@
 #![allow(clippy::too_many_arguments)]
 #![allow(clippy::type_complexity)]
 #![feature(generic_const_exprs)]
-#![allow(dead_code)]
 
 pub mod all_stark;
 pub mod config;
diff --git a/evm/src/memory/memory_stark.rs b/evm/src/memory/memory_stark.rs
index f05a2749..a9ccec0a 100644
--- a/evm/src/memory/memory_stark.rs
+++ b/evm/src/memory/memory_stark.rs
@@ -17,6 +17,7 @@ use crate::memory::registers::{
     SEGMENT_FIRST_CHANGE, SORTED_ADDR_CONTEXT, SORTED_ADDR_SEGMENT, SORTED_ADDR_VIRTUAL,
     SORTED_IS_READ, SORTED_TIMESTAMP, TIMESTAMP, VIRTUAL_FIRST_CHANGE,
 };
+use crate::permutation::PermutationPair;
 use crate::stark::Stark;
 use crate::util::{permuted_cols, trace_rows_to_poly_values};
 use crate::vars::{StarkEvaluationTargets, StarkEvaluationVars};
@@ -28,7 +29,16 @@ pub struct MemoryStark<F, const D: usize> {
     pub(crate) f: PhantomData<F>,
 }
 
-pub fn generate_random_memory_ops<F: RichField>(num_ops: usize) -> Vec<(F, F, F, F, F, [F; 8])> {
+pub struct MemoryOp<F> {
+    timestamp: F,
+    is_read: F,
+    context: F,
+    segment: F,
+    virt: F,
+    value: [F; 8],
+}
+
+pub fn generate_random_memory_ops<F: RichField>(num_ops: usize) -> Vec<MemoryOp<F>> {
     let mut memory_ops = Vec::new();
 
     let mut rng = thread_rng();
@@ -61,7 +71,14 @@ pub fn generate_random_memory_ops<F: RichField>(num_ops: usize) -> Vec<(F, F, F,
 
         let timestamp = F::from_canonical_usize(i);
 
-        memory_ops.push((timestamp, is_read_field, context, segment, virt, vals))
+        memory_ops.push(MemoryOp {
+            timestamp,
+            is_read: is_read_field,
+            context,
+            segment,
+            virt,
+            value: vals,
+        });
     }
 
     memory_ops
@@ -164,22 +181,27 @@ pub fn generate_range_check_value<F: RichField>(
 impl<F: RichField + Extendable<D>, const D: usize> MemoryStark<F, D> {
     pub(crate) fn generate_trace_rows(
         &self,
-        memory_ops: Vec<(F, F, F, F, F, [F; 8])>,
+        memory_ops: Vec<MemoryOp<F>>,
     ) -> Vec<[F; NUM_REGISTERS]> {
         let num_ops = memory_ops.len();
 
-        let mut trace_cols: [Vec<F>; NUM_REGISTERS] = vec![vec![F::ZERO; num_ops]; NUM_REGISTERS]
-            .try_into()
-            .unwrap();
+        let mut trace_cols = [(); NUM_REGISTERS].map(|_| vec![F::ZERO; num_ops]);
         for i in 0..num_ops {
-            let (timestamp, is_read, context, segment, virt, values) = memory_ops[i];
+            let MemoryOp {
+                timestamp,
+                is_read,
+                context,
+                segment,
+                virt,
+                value,
+            } = memory_ops[i];
             trace_cols[TIMESTAMP][i] = timestamp;
             trace_cols[IS_READ][i] = is_read;
             trace_cols[ADDR_CONTEXT][i] = context;
             trace_cols[ADDR_SEGMENT][i] = segment;
             trace_cols[ADDR_VIRTUAL][i] = virt;
             for j in 0..8 {
-                trace_cols[value_limb(j)][i] = values[j];
+                trace_cols[value_limb(j)][i] = value[j];
             }
         }
 
@@ -252,7 +274,7 @@ impl<F: RichField + Extendable<D>, const D: usize> MemoryStark<F, D> {
         trace_cols[VIRTUAL_FIRST_CHANGE] = virtual_first_change;
 
         trace_cols[RANGE_CHECK] = range_check_value;
-        trace_cols[COUNTER] = (0..trace_cols[0].len())
+        trace_cols[COUNTER] = (0..num_trace_rows)
             .map(|i| F::from_canonical_usize(i))
             .collect();
 
@@ -262,13 +284,10 @@ impl<F: RichField + Extendable<D>, const D: usize> MemoryStark<F, D> {
         trace_cols[COUNTER_PERMUTED] = permuted_table;
     }
 
-    pub fn generate_trace(
-        &self,
-        memory_ops: Vec<(F, F, F, F, F, [F; 8])>,
-    ) -> Vec<PolynomialValues<F>> {
+    pub fn generate_trace(&self, memory_ops: Vec<MemoryOp<F>>) -> Vec<PolynomialValues<F>> {
         let mut timing = TimingTree::new("generate trace", log::Level::Debug);
 
-        // Generate the witness, except for permuted columns in the lookup argument.
+        // Generate the witness.
         let trace_rows = timed!(
             &mut timing,
             "generate trace rows",
@@ -363,7 +382,7 @@ impl<F: RichField + Extendable<D>, const D: usize> Stark<F, D> for MemoryStark<F
         // Lookup argument for the range check.
         let local_perm_input = vars.local_values[RANGE_CHECK_PERMUTED];
         let next_perm_table = vars.next_values[COUNTER_PERMUTED];
-        let next_perm_input = vars.next_values[COUNTER_PERMUTED];
+        let next_perm_input = vars.next_values[RANGE_CHECK_PERMUTED];
 
         // A "vertical" diff between the local and next permuted inputs.
         let diff_input_prev = next_perm_input - local_perm_input;
@@ -513,6 +532,13 @@ impl<F: RichField + Extendable<D>, const D: usize> Stark<F, D> for MemoryStark<F
     fn constraint_degree(&self) -> usize {
         3
     }
+
+    fn permutation_pairs(&self) -> Vec<PermutationPair> {
+        vec![
+            PermutationPair::singletons(RANGE_CHECK, RANGE_CHECK_PERMUTED),
+            PermutationPair::singletons(COUNTER, COUNTER_PERMUTED),
+        ]
+    }
 }
 
 #[cfg(test)]
diff --git a/evm/src/memory/registers.rs b/evm/src/memory/registers.rs
index c81408c8..b89a9692 100644
--- a/evm/src/memory/registers.rs
+++ b/evm/src/memory/registers.rs
@@ -9,12 +9,14 @@ pub(crate) const ADDR_CONTEXT: usize = IS_READ + 1;
 pub(crate) const ADDR_SEGMENT: usize = ADDR_CONTEXT + 1;
 pub(crate) const ADDR_VIRTUAL: usize = ADDR_SEGMENT + 1;
 
+// Eight limbs to hold up to a 256-bit value.
 const VALUE_START: usize = ADDR_VIRTUAL + 1;
 pub(crate) const fn value_limb(i: usize) -> usize {
     debug_assert!(i < NUM_MEMORY_VALUE_LIMBS);
     VALUE_START + i
 }
 
+// Separate columns for the same memory operations, sorted by (addr, timestamp).
 pub(crate) const SORTED_TIMESTAMP: usize = VALUE_START + NUM_MEMORY_VALUE_LIMBS;
 pub(crate) const SORTED_IS_READ: usize = SORTED_TIMESTAMP + 1;
 pub(crate) const SORTED_ADDR_CONTEXT: usize = SORTED_IS_READ + 1;
@@ -27,15 +29,24 @@ pub(crate) const fn sorted_value_limb(i: usize) -> usize {
     SORTED_VALUE_START + i
 }
 
+// Flags to indicate whether this part of the address differs from the next row (in the sorted
+// columns), and the previous parts do not differ.
+// That is, e.g., `SEGMENT_FIRST_CHANGE` is `F::ONE` iff `SORTED_ADDR_CONTEXT` is the same in this
+// row and the next, but `SORTED_ADDR_SEGMENT` is not.
 pub(crate) const CONTEXT_FIRST_CHANGE: usize = SORTED_VALUE_START + NUM_MEMORY_VALUE_LIMBS;
 pub(crate) const SEGMENT_FIRST_CHANGE: usize = CONTEXT_FIRST_CHANGE + 1;
 pub(crate) const VIRTUAL_FIRST_CHANGE: usize = SEGMENT_FIRST_CHANGE + 1;
 
+// We use a range check to ensure sorting.
 pub(crate) const RANGE_CHECK: usize = VIRTUAL_FIRST_CHANGE + 1;
+// The counter column (used for the range check) starts from 0 and increments.
 pub(crate) const COUNTER: usize = RANGE_CHECK + 1;
+// Helper columns for the permutation argument used to enforce the range check.
 pub(crate) const RANGE_CHECK_PERMUTED: usize = COUNTER + 1;
 pub(crate) const COUNTER_PERMUTED: usize = RANGE_CHECK_PERMUTED + 1;
 
+// Flags to indicate if this operation corresponds to the `i`th memory op in a certain row of the
+// CPU table.
 const IS_MEMOP_START: usize = COUNTER_PERMUTED + 1;
 pub(crate) const fn is_memop(i: usize) -> usize {
     debug_assert!(i < NUM_MEMORY_OPS);