diff --git a/src/gates/mod.rs b/src/gates/mod.rs
index 7f7ee32b..93de5e97 100644
--- a/src/gates/mod.rs
+++ b/src/gates/mod.rs
@@ -20,6 +20,7 @@ pub(crate) mod poseidon_mds;
 pub(crate) mod public_input;
 pub mod random_access;
 pub mod reducing;
+pub mod reducing_extension;
 pub mod subtraction_u32;
 pub mod switch;
 
diff --git a/src/gates/reducing_extension.rs b/src/gates/reducing_extension.rs
new file mode 100644
index 00000000..532b484f
--- /dev/null
+++ b/src/gates/reducing_extension.rs
@@ -0,0 +1,222 @@
+use std::ops::Range;
+
+use crate::field::extension_field::target::ExtensionTarget;
+use crate::field::extension_field::Extendable;
+use crate::field::extension_field::FieldExtension;
+use crate::field::field_types::RichField;
+use crate::gates::gate::Gate;
+use crate::iop::generator::{GeneratedValues, SimpleGenerator, WitnessGenerator};
+use crate::iop::target::Target;
+use crate::iop::witness::{PartitionWitness, Witness};
+use crate::plonk::circuit_builder::CircuitBuilder;
+use crate::plonk::vars::{EvaluationTargets, EvaluationVars, EvaluationVarsBase};
+
+/// Computes `sum alpha^i c_i` for a vector `c_i` of `num_coeffs` elements of the extension field.
+#[derive(Debug, Clone)]
+pub struct ReducingExtensionGate<const D: usize> {
+    pub num_coeffs: usize,
+}
+
+impl<const D: usize> ReducingExtensionGate<D> {
+    pub fn new(num_coeffs: usize) -> Self {
+        Self { num_coeffs }
+    }
+
+    pub fn max_coeffs_len(num_wires: usize, num_routed_wires: usize) -> usize {
+        // `3*D` routed wires are used for the output, alpha and old accumulator.
+        // Need `num_coeffs*D` routed wires for coeffs, and `(num_coeffs-1)*D` wires for accumulators.
+        ((num_routed_wires - 3 * D) / D).min((num_wires - 2 * D) / (D * 2))
+    }
+
+    pub fn wires_output() -> Range<usize> {
+        0..D
+    }
+    pub fn wires_alpha() -> Range<usize> {
+        D..2 * D
+    }
+    pub fn wires_old_acc() -> Range<usize> {
+        2 * D..3 * D
+    }
+    const START_COEFFS: usize = 3 * D;
+    pub fn wires_coeff(i: usize) -> Range<usize> {
+        Self::START_COEFFS + i * D..Self::START_COEFFS + (i + 1) * D
+    }
+    fn start_accs(&self) -> usize {
+        Self::START_COEFFS + self.num_coeffs * D
+    }
+    fn wires_accs(&self, i: usize) -> Range<usize> {
+        debug_assert!(i < self.num_coeffs);
+        if i == self.num_coeffs - 1 {
+            // The last accumulator is the output.
+            return Self::wires_output();
+        }
+        self.start_accs() + D * i..self.start_accs() + D * (i + 1)
+    }
+}
+
+impl<F: RichField + Extendable<D>, const D: usize> Gate<F, D> for ReducingExtensionGate<D> {
+    fn id(&self) -> String {
+        format!("{:?}", self)
+    }
+
+    fn eval_unfiltered(&self, vars: EvaluationVars<F, D>) -> Vec<F::Extension> {
+        let alpha = vars.get_local_ext_algebra(Self::wires_alpha());
+        let old_acc = vars.get_local_ext_algebra(Self::wires_old_acc());
+        let coeffs = (0..self.num_coeffs)
+            .map(|i| vars.get_local_ext_algebra(Self::wires_coeff(i)))
+            .collect::<Vec<_>>();
+        let accs = (0..self.num_coeffs)
+            .map(|i| vars.get_local_ext_algebra(self.wires_accs(i)))
+            .collect::<Vec<_>>();
+
+        let mut constraints = Vec::with_capacity(<Self as Gate<F, D>>::num_constraints(self));
+        let mut acc = old_acc;
+        for i in 0..self.num_coeffs {
+            constraints.push(acc * alpha + coeffs[i] - accs[i]);
+            acc = accs[i];
+        }
+
+        constraints
+            .into_iter()
+            .flat_map(|alg| alg.to_basefield_array())
+            .collect()
+    }
+
+    fn eval_unfiltered_base(&self, vars: EvaluationVarsBase<F>) -> Vec<F> {
+        let alpha = vars.get_local_ext(Self::wires_alpha());
+        let old_acc = vars.get_local_ext(Self::wires_old_acc());
+        let coeffs = (0..self.num_coeffs)
+            .map(|i| vars.get_local_ext(Self::wires_coeff(i)))
+            .collect::<Vec<_>>();
+        let accs = (0..self.num_coeffs)
+            .map(|i| vars.get_local_ext(self.wires_accs(i)))
+            .collect::<Vec<_>>();
+
+        let mut constraints = Vec::with_capacity(<Self as Gate<F, D>>::num_constraints(self));
+        let mut acc = old_acc;
+        for i in 0..self.num_coeffs {
+            constraints.extend((acc * alpha + coeffs[i] - accs[i]).to_basefield_array());
+            acc = accs[i];
+        }
+
+        constraints
+    }
+
+    fn eval_unfiltered_recursively(
+        &self,
+        builder: &mut CircuitBuilder<F, D>,
+        vars: EvaluationTargets<D>,
+    ) -> Vec<ExtensionTarget<D>> {
+        let alpha = vars.get_local_ext_algebra(Self::wires_alpha());
+        let old_acc = vars.get_local_ext_algebra(Self::wires_old_acc());
+        let coeffs = (0..self.num_coeffs)
+            .map(|i| vars.get_local_ext_algebra(Self::wires_coeff(i)))
+            .collect::<Vec<_>>();
+        let accs = (0..self.num_coeffs)
+            .map(|i| vars.get_local_ext_algebra(self.wires_accs(i)))
+            .collect::<Vec<_>>();
+
+        let mut constraints = Vec::with_capacity(<Self as Gate<F, D>>::num_constraints(self));
+        let mut acc = old_acc;
+        for i in 0..self.num_coeffs {
+            let coeff = coeffs[i];
+            let mut tmp = builder.mul_add_ext_algebra(acc, alpha, coeff);
+            tmp = builder.sub_ext_algebra(tmp, accs[i]);
+            constraints.push(tmp);
+            acc = accs[i];
+        }
+
+        constraints
+            .into_iter()
+            .flat_map(|alg| alg.to_ext_target_array())
+            .collect()
+    }
+
+    fn generators(
+        &self,
+        gate_index: usize,
+        _local_constants: &[F],
+    ) -> Vec<Box<dyn WitnessGenerator<F>>> {
+        vec![Box::new(
+            ReducingGenerator {
+                gate_index,
+                gate: self.clone(),
+            }
+            .adapter(),
+        )]
+    }
+
+    fn num_wires(&self) -> usize {
+        2 * D + 2 * D * self.num_coeffs
+    }
+
+    fn num_constants(&self) -> usize {
+        0
+    }
+
+    fn degree(&self) -> usize {
+        2
+    }
+
+    fn num_constraints(&self) -> usize {
+        D * self.num_coeffs
+    }
+}
+
+#[derive(Debug)]
+struct ReducingGenerator<const D: usize> {
+    gate_index: usize,
+    gate: ReducingExtensionGate<D>,
+}
+
+impl<F: Extendable<D>, const D: usize> SimpleGenerator<F> for ReducingGenerator<D> {
+    fn dependencies(&self) -> Vec<Target> {
+        ReducingExtensionGate::<D>::wires_alpha()
+            .chain(ReducingExtensionGate::<D>::wires_old_acc())
+            .chain((0..self.gate.num_coeffs).flat_map(ReducingExtensionGate::<D>::wires_coeff))
+            .map(|i| Target::wire(self.gate_index, i))
+            .collect()
+    }
+
+    fn run_once(&self, witness: &PartitionWitness<F>, out_buffer: &mut GeneratedValues<F>) {
+        let local_extension = |range: Range<usize>| -> F::Extension {
+            let t = ExtensionTarget::from_range(self.gate_index, range);
+            witness.get_extension_target(t)
+        };
+
+        let alpha = local_extension(ReducingExtensionGate::<D>::wires_alpha());
+        let old_acc = local_extension(ReducingExtensionGate::<D>::wires_old_acc());
+        let coeffs = (0..self.gate.num_coeffs)
+            .map(|i| local_extension(ReducingExtensionGate::<D>::wires_coeff(i)))
+            .collect::<Vec<_>>();
+        let accs = (0..self.gate.num_coeffs)
+            .map(|i| ExtensionTarget::from_range(self.gate_index, self.gate.wires_accs(i)))
+            .collect::<Vec<_>>();
+
+        let mut acc = old_acc;
+        for i in 0..self.gate.num_coeffs {
+            let computed_acc = acc * alpha + coeffs[i];
+            out_buffer.set_extension_target(accs[i], computed_acc);
+            acc = computed_acc;
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use anyhow::Result;
+
+    use crate::field::goldilocks_field::GoldilocksField;
+    use crate::gates::gate_testing::{test_eval_fns, test_low_degree};
+    use crate::gates::reducing_extension::ReducingExtensionGate;
+
+    #[test]
+    fn low_degree() {
+        test_low_degree::<GoldilocksField, _, 4>(ReducingExtensionGate::new(22));
+    }
+
+    #[test]
+    fn eval_fns() -> Result<()> {
+        test_eval_fns::<GoldilocksField, _, 4>(ReducingExtensionGate::new(22))
+    }
+}
diff --git a/src/util/reducing.rs b/src/util/reducing.rs
index 3e00602c..f700a6ff 100644
--- a/src/util/reducing.rs
+++ b/src/util/reducing.rs
@@ -3,7 +3,9 @@ use std::borrow::Borrow;
 use crate::field::extension_field::target::ExtensionTarget;
 use crate::field::extension_field::Extendable;
 use crate::field::field_types::{Field, RichField};
+use crate::gates::arithmetic_extension::ArithmeticExtensionGate;
 use crate::gates::reducing::ReducingGate;
+use crate::gates::reducing_extension::ReducingExtensionGate;
 use crate::iop::target::Target;
 use crate::plonk::circuit_builder::CircuitBuilder;
 use crate::polynomial::polynomial::PolynomialCoeffs;
@@ -93,7 +95,7 @@ impl<const D: usize> ReducingFactorTarget<D> {
         Self { base, count: 0 }
     }
 
-    /// Reduces a length `n` vector of `Target`s using `n/21` `ReducingGate`s (with 33 routed wires and 126 wires).
+    /// Reduces a vector of `Target`s using `ReducingGate`s.
     pub fn reduce_base<F>(
         &mut self,
         terms: &[Target],
@@ -102,11 +104,22 @@ impl<const D: usize> ReducingFactorTarget<D> {
     where
         F: RichField + Extendable<D>,
     {
+        let l = terms.len();
+
+        // For small reductions, use an arithmetic gate.
+        if l <= ArithmeticExtensionGate::<D>::new_from_config(&builder.config).num_ops + 1 {
+            let terms_ext = terms
+                .iter()
+                .map(|&t| builder.convert_to_ext(t))
+                .collect::<Vec<_>>();
+            return self.reduce_arithmetic(&terms_ext, builder);
+        }
+
         let max_coeffs_len = ReducingGate::<D>::max_coeffs_len(
             builder.config.num_wires,
             builder.config.num_routed_wires,
         );
-        self.count += terms.len() as u64;
+        self.count += l as u64;
         let zero = builder.zero();
         let zero_ext = builder.zero_extension();
         let mut acc = zero_ext;
@@ -137,6 +150,7 @@ impl<const D: usize> ReducingFactorTarget<D> {
         acc
     }
 
+    /// Reduces a vector of `ExtensionTarget`s using `ReducingExtensionGate`s.
     pub fn reduce<F>(
         &mut self,
         terms: &[ExtensionTarget<D>], // Could probably work with a `DoubleEndedIterator` too.
@@ -146,18 +160,74 @@ impl<const D: usize> ReducingFactorTarget<D> {
         F: RichField + Extendable<D>,
     {
         let l = terms.len();
-        self.count += l as u64;
 
-        let mut terms_vec = terms.to_vec();
-        let mut acc = builder.zero_extension();
-        terms_vec.reverse();
-
-        for x in terms_vec {
-            acc = builder.mul_add_extension(self.base, acc, x);
+        // For small reductions, use an arithmetic gate.
+        if l <= ArithmeticExtensionGate::<D>::new_from_config(&builder.config).num_ops + 1 {
+            return self.reduce_arithmetic(terms, builder);
         }
+
+        let max_coeffs_len = ReducingExtensionGate::<D>::max_coeffs_len(
+            builder.config.num_wires,
+            builder.config.num_routed_wires,
+        );
+        self.count += l as u64;
+        let zero_ext = builder.zero_extension();
+        let mut acc = zero_ext;
+        let mut reversed_terms = terms.to_vec();
+        while reversed_terms.len() % max_coeffs_len != 0 {
+            reversed_terms.push(zero_ext);
+        }
+        reversed_terms.reverse();
+        for chunk in reversed_terms.chunks_exact(max_coeffs_len) {
+            let gate = ReducingExtensionGate::new(max_coeffs_len);
+            let gate_index = builder.add_gate(gate.clone(), Vec::new());
+
+            builder.connect_extension(
+                self.base,
+                ExtensionTarget::from_range(gate_index, ReducingExtensionGate::<D>::wires_alpha()),
+            );
+            builder.connect_extension(
+                acc,
+                ExtensionTarget::from_range(
+                    gate_index,
+                    ReducingExtensionGate::<D>::wires_old_acc(),
+                ),
+            );
+            for (i, &t) in chunk.iter().enumerate() {
+                builder.connect_extension(
+                    t,
+                    ExtensionTarget::from_range(
+                        gate_index,
+                        ReducingExtensionGate::<D>::wires_coeff(i),
+                    ),
+                );
+            }
+
+            acc =
+                ExtensionTarget::from_range(gate_index, ReducingExtensionGate::<D>::wires_output());
+        }
+
         acc
     }
 
+    /// Reduces a vector of `ExtensionTarget`s using `ArithmeticGate`s.
+    fn reduce_arithmetic<F>(
+        &mut self,
+        terms: &[ExtensionTarget<D>],
+        builder: &mut CircuitBuilder<F, D>,
+    ) -> ExtensionTarget<D>
+    where
+        F: RichField + Extendable<D>,
+    {
+        self.count += terms.len() as u64;
+        terms
+            .iter()
+            .rev()
+            .fold(builder.zero_extension(), |acc, &et| {
+                builder.mul_add_extension(self.base, acc, et)
+            })
+    }
+
     pub fn shift<F>(
         &mut self,
         x: ExtensionTarget<D>,
@@ -260,4 +330,9 @@ mod tests {
     fn test_reduce_gadget_base_100() -> Result<()> {
         test_reduce_gadget_base(100)
     }
+
+    #[test]
+    fn test_reduce_gadget_100() -> Result<()> {
+        test_reduce_gadget(100)
+    }
 }