diff --git a/plonky2/src/gadgets/lookup.rs b/plonky2/src/gadgets/lookup.rs
index 3a3bba8da5..cc60cbe7ea 100644
--- a/plonky2/src/gadgets/lookup.rs
+++ b/plonky2/src/gadgets/lookup.rs
@@ -1,8 +1,6 @@
-use alloc::sync::Arc;
-
 use crate::field::extension::Extendable;
 use crate::gates::lookup::LookupGate;
-use crate::gates::lookup_table::LookupTableGate;
+use crate::gates::lookup_table::{LookupTable, LookupTableGate};
 use crate::gates::noop::NoopGate;
 use crate::hash::hash_types::RichField;
 use crate::iop::target::Target;
@@ -47,7 +45,7 @@ pub const SMALLER_TABLE: [u16; 8] = [2, 24, 56, 100, 128, 16, 20, 49];
 
 impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     /// Adds a lookup table to the list of stored lookup tables `self.luts` based on a table of (input, output) pairs. It returns the index of the LUT within `self.luts`.
-    pub fn add_lookup_table_from_pairs(&mut self, table: Arc<Vec<(u16, u16)>>) -> usize {
+    pub fn add_lookup_table_from_pairs(&mut self, table: LookupTable) -> usize {
         self.update_luts_from_pairs(table)
     }
 
diff --git a/plonky2/src/gates/lookup.rs b/plonky2/src/gates/lookup.rs
index cbf0049099..0ecac5018e 100644
--- a/plonky2/src/gates/lookup.rs
+++ b/plonky2/src/gates/lookup.rs
@@ -4,6 +4,7 @@ use alloc::sync::Arc;
 use alloc::vec::Vec;
 use core::usize;
 
+use super::lookup_table::LookupTable;
 use crate::field::extension::Extendable;
 use crate::field::packed::PackedField;
 use crate::gates::gate::Gate;
@@ -22,17 +23,19 @@ use crate::plonk::vars::{
 };
 use crate::util::serialization::{Buffer, IoResult, Read, Write};
 
+pub type Lookup = Vec<(Target, Target)>;
+
 /// A gate which stores (input, output) lookup pairs made elsewhere in the trace. It doesn't check any constraints itself.
 #[derive(Debug, Clone)]
 pub struct LookupGate {
     /// Number of lookups per gate.
     pub num_slots: usize,
     /// LUT associated to the gate.
-    lut: Arc<Vec<(u16, u16)>>,
+    lut: LookupTable,
 }
 
 impl LookupGate {
-    pub fn new_from_table(config: &CircuitConfig, lut: Arc<Vec<(u16, u16)>>) -> Self {
+    pub fn new_from_table(config: &CircuitConfig, lut: LookupTable) -> Self {
         Self {
             num_slots: Self::num_slots(config),
             lut,
@@ -142,7 +145,7 @@ impl<F: RichField + Extendable<D>, const D: usize> PackedEvaluableBase<F, D> for
 #[derive(Clone, Debug, Default)]
 pub struct LookupGenerator {
     row: usize,
-    lut: Arc<Vec<(u16, u16)>>,
+    lut: LookupTable,
     slot_nb: usize,
 }
 
diff --git a/plonky2/src/gates/lookup_table.rs b/plonky2/src/gates/lookup_table.rs
index 3869e2f260..b4ad902ab8 100644
--- a/plonky2/src/gates/lookup_table.rs
+++ b/plonky2/src/gates/lookup_table.rs
@@ -24,23 +24,21 @@ use crate::plonk::vars::{
 };
 use crate::util::serialization::{Buffer, IoResult, Read, Write};
 
+pub type LookupTable = Arc<Vec<(u16, u16)>>;
+
 /// A gate which stores the set of (input, output) value pairs of a lookup table, and their multiplicities.
 #[derive(Debug, Clone)]
 pub struct LookupTableGate {
     /// Number of lookup entries per gate.
     pub num_slots: usize,
     /// Lookup table associated to the gate.
-    pub lut: Arc<Vec<(u16, u16)>>,
+    pub lut: LookupTable,
     /// First row of the lookup table.
     last_lut_row: usize,
 }
 
 impl LookupTableGate {
-    pub fn new_from_table(
-        config: &CircuitConfig,
-        lut: Arc<Vec<(u16, u16)>>,
-        last_lut_row: usize,
-    ) -> Self {
+    pub fn new_from_table(config: &CircuitConfig, lut: LookupTable, last_lut_row: usize) -> Self {
         Self {
             num_slots: Self::num_slots(config),
             lut,
@@ -164,7 +162,7 @@ impl<F: RichField + Extendable<D>, const D: usize> PackedEvaluableBase<F, D> for
 #[derive(Clone, Debug, Default)]
 pub struct LookupTableGenerator {
     row: usize,
-    lut: Arc<Vec<(u16, u16)>>,
+    lut: LookupTable,
     slot_nb: usize,
     num_slots: usize,
     last_lut_row: usize,
diff --git a/plonky2/src/lookup_test.rs b/plonky2/src/lookup_test.rs
index e220451ffd..04b5720383 100644
--- a/plonky2/src/lookup_test.rs
+++ b/plonky2/src/lookup_test.rs
@@ -9,6 +9,7 @@ mod tests {
     use log::{Level, LevelFilter};
 
     use crate::gadgets::lookup::{OTHER_TABLE, SMALLER_TABLE, TIP5_TABLE};
+    use crate::gates::lookup_table::LookupTable;
     use crate::gates::noop::NoopGate;
     use crate::plonk::prover::prove;
     use crate::util::timing::TimingTree;
@@ -54,7 +55,7 @@ mod tests {
 
         LOGGER_INITIALIZED.call_once(|| init_logger().unwrap());
         let tip5_table = TIP5_TABLE.to_vec();
-        let table: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(tip5_table).collect());
+        let table: LookupTable = Arc::new((0..256).zip_eq(tip5_table).collect());
         let config = CircuitConfig::standard_recursion_config();
         let mut builder = CircuitBuilder::<F, D>::new(config);
 
@@ -129,7 +130,7 @@ mod tests {
         let first_out = tip5_table[look_val_a];
         let second_out = tip5_table[look_val_b];
 
-        let table: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(tip5_table).collect());
+        let table: LookupTable = Arc::new((0..256).zip_eq(tip5_table).collect());
 
         let other_table = OTHER_TABLE.to_vec();
 
@@ -142,7 +143,7 @@ mod tests {
         let s = first_out + second_out;
         let final_out = other_table[s as usize];
 
-        let table2: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(other_table).collect());
+        let table2: LookupTable = Arc::new((0..256).zip_eq(other_table).collect());
         let table2_index = builder.add_lookup_table_from_pairs(table2);
 
         let output_final = builder.add_lookup_from_index(sum, table2_index);
@@ -208,11 +209,11 @@ mod tests {
         let init_b = 2;
 
         let tab: Vec<u16> = SMALLER_TABLE.to_vec();
-        let table: Arc<Vec<(u16, u16)>> = Arc::new((2..10).zip_eq(tab).collect());
+        let table: LookupTable = Arc::new((2..10).zip_eq(tab).collect());
 
         let other_table = OTHER_TABLE.to_vec();
 
-        let table2: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(other_table).collect());
+        let table2: LookupTable = Arc::new((0..256).zip_eq(other_table).collect());
         let small_index = builder.add_lookup_table_from_pairs(table.clone());
         let output_a = builder.add_lookup_from_index(initial_a, small_index);
 
@@ -293,7 +294,7 @@ mod tests {
         let look_val_b = 2;
 
         let tip5_table = TIP5_TABLE.to_vec();
-        let table: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(tip5_table).collect());
+        let table: LookupTable = Arc::new((0..256).zip_eq(tip5_table).collect());
 
         let out_a = table[look_val_a].1;
         let out_b = table[look_val_b].1;
@@ -310,7 +311,7 @@ mod tests {
 
         let other_table = OTHER_TABLE.to_vec();
 
-        let table2: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(other_table).collect());
+        let table2: LookupTable = Arc::new((0..256).zip_eq(other_table).collect());
 
         let s = out_a + out_b;
         let out_final = table2[s as usize].1;
@@ -384,7 +385,7 @@ mod tests {
         let look_val_b = 2;
 
         let tip5_table = TIP5_TABLE.to_vec();
-        let table: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(tip5_table).collect());
+        let table: LookupTable = Arc::new((0..256).zip_eq(tip5_table).collect());
 
         let table_index = builder.add_lookup_table_from_pairs(table.clone());
         let output_a = builder.add_lookup_from_index(initial_a, table_index);
diff --git a/plonky2/src/plonk/circuit_builder.rs b/plonky2/src/plonk/circuit_builder.rs
index db9f1cf5f6..8955a2bdb9 100644
--- a/plonky2/src/plonk/circuit_builder.rs
+++ b/plonky2/src/plonk/circuit_builder.rs
@@ -25,7 +25,8 @@ use crate::gates::arithmetic_base::ArithmeticGate;
 use crate::gates::arithmetic_extension::ArithmeticExtensionGate;
 use crate::gates::constant::ConstantGate;
 use crate::gates::gate::{CurrentSlot, Gate, GateInstance, GateRef};
-use crate::gates::lookup::LookupGate;
+use crate::gates::lookup::{Lookup, LookupGate};
+use crate::gates::lookup_table::LookupTable;
 use crate::gates::noop::NoopGate;
 use crate::gates::public_input::PublicInputGate;
 use crate::gates::selectors::{selector_ends_lookups, selector_polynomials, selectors_lookup};
@@ -129,10 +130,10 @@ pub struct CircuitBuilder<F: RichField + Extendable<D>, const D: usize> {
     lookup_rows: Vec<LookupWire>,
 
     /// For each LUT index, vector of `(looking_in, looking_out)` pairs.
-    lut_to_lookups: Vec<Vec<(Target, Target)>>,
+    lut_to_lookups: Vec<Lookup>,
 
     // Lookup tables in the form of `Vec<(input_value, output_value)>`.
-    luts: Vec<Arc<Vec<(u16, u16)>>>,
+    luts: Vec<LookupTable>,
 
     /// Optional common data. When it is `Some(goal_data)`, the `build` function panics if the resulting
     /// common data doesn't equal `goal_data`.
@@ -581,12 +582,12 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     }
 
     /// Checks whether a LUT is already stored in `self.luts`
-    pub fn is_stored(&self, lut: Arc<Vec<(u16, u16)>>) -> Option<usize> {
+    pub fn is_stored(&self, lut: LookupTable) -> Option<usize> {
         self.luts.iter().position(|elt| *elt == lut)
     }
 
     /// Returns the LUT at index `idx`.
-    pub fn get_lut(&self, idx: usize) -> Arc<Vec<(u16, u16)>> {
+    pub fn get_lut(&self, idx: usize) -> LookupTable {
         assert!(
             idx < self.luts.len(),
             "index idx: {} greater than the total number of created LUTS: {}",
@@ -632,7 +633,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
             .copied()
             .zip_eq(table.iter().copied())
             .collect();
-        let lut: Arc<Vec<(u16, u16)>> = Arc::new(pairs);
+        let lut: LookupTable = Arc::new(pairs);
 
         // If the LUT `lut` is already stored in `self.luts`, return its index. Otherwise, append `table` to `self.luts` and return its index.
         if let Some(idx) = self.is_stored(lut.clone()) {
@@ -646,7 +647,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     }
 
     /// Adds a table to the vector of LUTs in the circuit builder.
-    pub fn update_luts_from_pairs(&mut self, table: Arc<Vec<(u16, u16)>>) -> usize {
+    pub fn update_luts_from_pairs(&mut self, table: LookupTable) -> usize {
         // If the LUT `table` is already stored in `self.luts`, return its index. Otherwise, append `table` to `self.luts` and return its index.
         if let Some(idx) = self.is_stored(table.clone()) {
             idx
diff --git a/plonky2/src/plonk/circuit_data.rs b/plonky2/src/plonk/circuit_data.rs
index e713265641..7d91a3a3be 100644
--- a/plonky2/src/plonk/circuit_data.rs
+++ b/plonky2/src/plonk/circuit_data.rs
@@ -1,5 +1,4 @@
 use alloc::collections::BTreeMap;
-use alloc::sync::Arc;
 use alloc::vec;
 use alloc::vec::Vec;
 use core::ops::{Range, RangeFrom};
@@ -19,6 +18,8 @@ use crate::fri::structure::{
 };
 use crate::fri::{FriConfig, FriParams};
 use crate::gates::gate::GateRef;
+use crate::gates::lookup::Lookup;
+use crate::gates::lookup_table::LookupTable;
 use crate::gates::selectors::SelectorsInfo;
 use crate::hash::hash_types::{HashOutTarget, MerkleCapTarget, RichField};
 use crate::hash::merkle_tree::MerkleCap;
@@ -317,7 +318,7 @@ pub struct ProverOnlyCircuitData<
     ///The concrete placement of the lookup gates for each lookup table index.
     pub lookup_rows: Vec<LookupWire>,
     /// A vector of (looking_in, looking_out) pairs for for each lookup table index.
-    pub lut_to_lookups: Vec<Vec<(Target, Target)>>,
+    pub lut_to_lookups: Vec<Lookup>,
 }
 
 /// Circuit data required by the verifier, but not the prover.
@@ -380,7 +381,7 @@ pub struct CommonCircuitData<F: RichField + Extendable<D>, const D: usize> {
     pub num_lookup_selectors: usize,
 
     /// The stored lookup tables.
-    pub luts: Vec<Arc<Vec<(u16, u16)>>>,
+    pub luts: Vec<LookupTable>,
 }
 
 impl<F: RichField + Extendable<D>, const D: usize> CommonCircuitData<F, D> {
diff --git a/plonky2/src/plonk/proof.rs b/plonky2/src/plonk/proof.rs
index f9d5f1d1e7..bf70cacabc 100644
--- a/plonky2/src/plonk/proof.rs
+++ b/plonky2/src/plonk/proof.rs
@@ -456,6 +456,7 @@ mod tests {
 
     use crate::field::types::Sample;
     use crate::fri::reduction_strategies::FriReductionStrategy;
+    use crate::gates::lookup_table::LookupTable;
     use crate::gates::noop::NoopGate;
     use crate::iop::witness::PartialWitness;
     use crate::plonk::circuit_builder::CircuitBuilder;
@@ -529,7 +530,7 @@ mod tests {
             241, 25, 149, 105, 156, 51, 53, 168, 145, 247, 223, 79, 78, 226, 15, 222, 82, 115, 70,
             210, 27, 41, 1, 170, 40, 131, 192, 229, 248, 255,
         ];
-        let table: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(tip5_table).collect());
+        let table: LookupTable = Arc::new((0..256).zip_eq(tip5_table).collect());
         let config = CircuitConfig::standard_recursion_config();
         let mut builder = CircuitBuilder::<F, D>::new(config);
         let lut_index = builder.add_lookup_table_from_pairs(table);
diff --git a/plonky2/src/recursion/recursive_verifier.rs b/plonky2/src/recursion/recursive_verifier.rs
index 94a35080d2..613766e455 100644
--- a/plonky2/src/recursion/recursive_verifier.rs
+++ b/plonky2/src/recursion/recursive_verifier.rs
@@ -201,6 +201,7 @@ mod tests {
     use crate::fri::reduction_strategies::FriReductionStrategy;
     use crate::fri::FriConfig;
     use crate::gadgets::lookup::{OTHER_TABLE, TIP5_TABLE};
+    use crate::gates::lookup_table::LookupTable;
     use crate::gates::noop::NoopGate;
     use crate::iop::witness::{PartialWitness, WitnessWrite};
     use crate::plonk::circuit_data::{CircuitConfig, VerifierOnlyCircuitData};
@@ -421,7 +422,7 @@ mod tests {
         let look_val_b = 2;
 
         let tip5_table = TIP5_TABLE.to_vec();
-        let table: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(tip5_table).collect());
+        let table: LookupTable = Arc::new((0..256).zip_eq(tip5_table).collect());
 
         let out_a = table[look_val_a].1;
         let out_b = table[look_val_b].1;
@@ -482,7 +483,7 @@ mod tests {
         let first_out = tip5_table[look_val_a];
         let second_out = tip5_table[look_val_b];
 
-        let table: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(tip5_table).collect());
+        let table: LookupTable = Arc::new((0..256).zip_eq(tip5_table).collect());
 
         let other_table = OTHER_TABLE.to_vec();
 
@@ -495,7 +496,7 @@ mod tests {
         let s = first_out + second_out;
         let final_out = other_table[s as usize];
 
-        let table2: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(other_table).collect());
+        let table2: LookupTable = Arc::new((0..256).zip_eq(other_table).collect());
 
         let other_index = builder.add_lookup_table_from_pairs(table2);
         let output_final = builder.add_lookup_from_index(sum, other_index);
@@ -556,7 +557,7 @@ mod tests {
         let look_val_b = 2;
 
         let tip5_table = TIP5_TABLE.to_vec();
-        let table: Arc<Vec<(u16, u16)>> = Arc::new((0..256).zip_eq(tip5_table).collect());
+        let table: LookupTable = Arc::new((0..256).zip_eq(tip5_table).collect());
 
         let out_a = table[look_val_a].1;
         let out_b = table[look_val_b].1;
diff --git a/plonky2/src/util/serialization/mod.rs b/plonky2/src/util/serialization/mod.rs
index 8cce51e634..7c8141769c 100644
--- a/plonky2/src/util/serialization/mod.rs
+++ b/plonky2/src/util/serialization/mod.rs
@@ -31,6 +31,7 @@ use crate::fri::reduction_strategies::FriReductionStrategy;
 use crate::fri::{FriConfig, FriParams};
 use crate::gadgets::polynomial::PolynomialCoeffsExtTarget;
 use crate::gates::gate::GateRef;
+use crate::gates::lookup::Lookup;
 use crate::gates::selectors::SelectorsInfo;
 use crate::hash::hash_types::{HashOutTarget, MerkleCapTarget, RichField};
 use crate::hash::merkle_proofs::{MerkleProof, MerkleProofTarget};
@@ -1152,9 +1153,9 @@ pub trait Read {
         Ok(lut)
     }
 
-    /// Reads a target lookup table stored as `Vec<(Target, Target)>` from `self`.
+    /// Reads a target lookup table stored as `Lookup` from `self`.
     #[inline]
-    fn read_target_lut(&mut self) -> IoResult<Vec<(Target, Target)>> {
+    fn read_target_lut(&mut self) -> IoResult<Lookup> {
         let length = self.read_usize()?;
         let mut lut = Vec::with_capacity(length);
         for _ in 0..length {