diff --git a/evm/src/cpu/shift.rs b/evm/src/cpu/shift.rs
index a424929798..0f92cbd20d 100644
--- a/evm/src/cpu/shift.rs
+++ b/evm/src/cpu/shift.rs
@@ -19,8 +19,8 @@ pub(crate) fn eval_packed<P: PackedField>(
 
     // Not needed here; val is the input and we're verifying that output is
     // val * 2^d (mod 2^256)
-    //let val = lv.mem_channels[0];
-    //let output = lv.mem_channels[NUM_GP_CHANNELS - 1];
+    // let val = lv.mem_channels[0];
+    // let output = lv.mem_channels[NUM_GP_CHANNELS - 1];
 
     let shift_table_segment = P::Scalar::from_canonical_u64(Segment::ShiftTable as u64);
 
@@ -28,7 +28,7 @@ pub(crate) fn eval_packed<P: PackedField>(
     // two_exp.used is true (1) if the high limbs of the displacement are
     // zero and false (0) otherwise.
     let high_limbs_are_zero = two_exp.used;
-    yield_constr.constraint(is_shift * (two_exp.is_read - P::ONES));
+    yield_constr.constraint(is_shift * high_limbs_are_zero * (two_exp.is_read - P::ONES));
 
     let high_limbs_sum: P = displacement.value[1..].iter().copied().sum();
     let high_limbs_sum_inv = lv.general.shift().high_limb_sum_inv;
@@ -70,14 +70,20 @@ pub(crate) fn eval_ext_circuit<F: RichField + Extendable<D>, const D: usize>(
 
     let shift_table_segment = F::from_canonical_u64(Segment::ShiftTable as u64);
 
+    // Only lookup the shifting factor when displacement is < 2^32.
+    // two_exp.used is true (1) if the high limbs of the displacement are
+    // zero and false (0) otherwise.
     let high_limbs_are_zero = two_exp.used;
     let one = builder.one_extension();
     let t = builder.sub_extension(two_exp.is_read, one);
+    let t = builder.mul_extension(high_limbs_are_zero, t);
     let t = builder.mul_extension(is_shift, t);
     yield_constr.constraint(builder, t);
 
     let high_limbs_sum = builder.add_many_extension(&displacement.value[1..]);
     let high_limbs_sum_inv = lv.general.shift().high_limb_sum_inv;
+    // Verify that high_limbs_are_zero = 0 implies high_limbs_sum != 0 and
+    // high_limbs_are_zero = 1 implies high_limbs_sum = 0.
     let t = builder.one_extension();
     let t = builder.sub_extension(t, high_limbs_are_zero);
     let t = builder.mul_sub_extension(high_limbs_sum, high_limbs_sum_inv, t);
@@ -87,6 +93,9 @@ pub(crate) fn eval_ext_circuit<F: RichField + Extendable<D>, const D: usize>(
     let t = builder.mul_many_extension([is_shift, high_limbs_sum, high_limbs_are_zero]);
     yield_constr.constraint(builder, t);
 
+    // When the shift displacement is < 2^32, constrain the two_exp
+    // mem_channel to be the entry corresponding to `displacement` in
+    // the shift table lookup (will be zero if displacement >= 256).
     let t = builder.mul_extension(is_shift, two_exp.addr_context);
     yield_constr.constraint(builder, t);
     let t = builder.arithmetic_extension(
@@ -101,6 +110,7 @@ pub(crate) fn eval_ext_circuit<F: RichField + Extendable<D>, const D: usize>(
     let t = builder.mul_extension(is_shift, t);
     yield_constr.constraint(builder, t);
 
+    // Other channels must be unused
     for chan in &lv.mem_channels[3..NUM_GP_CHANNELS - 1] {
         let t = builder.mul_extension(is_shift, chan.used);
         yield_constr.constraint(builder, t);
diff --git a/evm/src/witness/operation.rs b/evm/src/witness/operation.rs
index 568fe4b181..f4dc03e806 100644
--- a/evm/src/witness/operation.rs
+++ b/evm/src/witness/operation.rs
@@ -497,6 +497,10 @@ fn append_shift<F: Field>(
         channel.addr_context = F::from_canonical_usize(lookup_addr.context);
         channel.addr_segment = F::from_canonical_usize(lookup_addr.segment);
         channel.addr_virtual = F::from_canonical_usize(lookup_addr.virt);
+
+        // Extra field required by the constraints for large shifts.
+        let high_limb_sum = row.mem_channels[0].value[1..].iter().copied().sum::<F>();
+        row.general.shift_mut().high_limb_sum_inv = high_limb_sum.inverse();
     }
 
     let operator = if is_shl {