diff --git a/plonky2/src/gates/gate.rs b/plonky2/src/gates/gate.rs
index f5de3472..e95ec0f8 100644
--- a/plonky2/src/gates/gate.rs
+++ b/plonky2/src/gates/gate.rs
@@ -1,6 +1,7 @@
 use std::collections::HashMap;
 use std::fmt::{Debug, Error, Formatter};
 use std::hash::{Hash, Hasher};
+use std::ops::Range;
 use std::sync::Arc;
 
 use plonky2_field::batch_util::batch_multiply_inplace;
@@ -85,13 +86,14 @@ pub trait Gate<F: RichField + Extendable<D>, const D: usize>: 'static + Send + S
         mut vars: EvaluationVars<F, D>,
         gate_index: usize,
         selector_index: usize,
-        group_range: (usize, usize),
+        group_range: Range<usize>,
         num_selectors: usize,
     ) -> Vec<F::Extension> {
         let filter = compute_filter(
             gate_index,
             group_range,
             vars.local_constants[selector_index],
+            num_selectors > 1,
         );
         vars.remove_prefix(num_selectors);
         self.eval_unfiltered(vars)
@@ -107,7 +109,7 @@ pub trait Gate<F: RichField + Extendable<D>, const D: usize>: 'static + Send + S
         mut vars_batch: EvaluationVarsBaseBatch<F>,
         gate_index: usize,
         selector_index: usize,
-        group_range: (usize, usize),
+        group_range: Range<usize>,
         num_selectors: usize,
     ) -> Vec<F> {
         let filters: Vec<_> = vars_batch
@@ -115,8 +117,9 @@ pub trait Gate<F: RichField + Extendable<D>, const D: usize>: 'static + Send + S
             .map(|vars| {
                 compute_filter(
                     gate_index,
-                    group_range,
+                    group_range.clone(),
                     vars.local_constants[selector_index],
+                    num_selectors > 1,
                 )
             })
             .collect();
@@ -135,7 +138,7 @@ pub trait Gate<F: RichField + Extendable<D>, const D: usize>: 'static + Send + S
         mut vars: EvaluationTargets<D>,
         gate_index: usize,
         selector_index: usize,
-        group_range: (usize, usize),
+        group_range: Range<usize>,
         num_selectors: usize,
         combined_gate_constraints: &mut [ExtensionTarget<D>],
     ) {
@@ -144,6 +147,7 @@ pub trait Gate<F: RichField + Extendable<D>, const D: usize>: 'static + Send + S
             gate_index,
             group_range,
             vars.local_constants[selector_index],
+            num_selectors > 1,
         );
         vars.remove_prefix(num_selectors);
         let my_constraints = self.eval_unfiltered_recursively(builder, vars);
@@ -231,11 +235,16 @@ pub struct PrefixedGate<F: RichField + Extendable<D>, const D: usize> {
 }
 
 /// A gate's filter designed so that it is non-zero if `s = gate_index`.
-fn compute_filter<K: Field>(gate_index: usize, group_range: (usize, usize), s: K) -> K {
-    debug_assert!((group_range.0 <= gate_index) && (gate_index < group_range.1));
-    (group_range.0..group_range.1)
+fn compute_filter<K: Field>(
+    gate_index: usize,
+    group_range: Range<usize>,
+    s: K,
+    many_selector: bool,
+) -> K {
+    debug_assert!(group_range.contains(&gate_index));
+    group_range
         .filter(|&i| i != gate_index)
-        .chain(Some(UNUSED_SELECTOR))
+        .chain(many_selector.then(|| UNUSED_SELECTOR))
         .map(|i| K::from_canonical_usize(i) - s)
         .product()
 }
@@ -243,13 +252,14 @@ fn compute_filter<K: Field>(gate_index: usize, group_range: (usize, usize), s: K
 fn compute_filter_recursively<F: RichField + Extendable<D>, const D: usize>(
     builder: &mut CircuitBuilder<F, D>,
     gate_index: usize,
-    group_range: (usize, usize),
+    group_range: Range<usize>,
     s: ExtensionTarget<D>,
+    many_selectors: bool,
 ) -> ExtensionTarget<D> {
-    debug_assert!((group_range.0 <= gate_index) && (gate_index < group_range.1));
-    let v = (group_range.0..group_range.1)
+    debug_assert!(group_range.contains(&gate_index));
+    let v = group_range
         .filter(|&i| i != gate_index)
-        .chain(Some(UNUSED_SELECTOR))
+        .chain(many_selectors.then(|| UNUSED_SELECTOR))
         .map(|i| {
             let c = builder.constant_extension(F::Extension::from_canonical_usize(i));
             builder.sub_extension(c, s)
diff --git a/plonky2/src/gates/selectors.rs b/plonky2/src/gates/selectors.rs
index f51bc8cb..559dcf48 100644
--- a/plonky2/src/gates/selectors.rs
+++ b/plonky2/src/gates/selectors.rs
@@ -1,3 +1,5 @@
+use std::ops::Range;
+
 use plonky2_field::extension_field::Extendable;
 use plonky2_field::polynomial::PolynomialValues;
 
@@ -10,7 +12,7 @@ pub(crate) const UNUSED_SELECTOR: usize = u32::MAX as usize;
 #[derive(Debug, Clone)]
 pub(crate) struct SelectorsInfo {
     pub(crate) selector_indices: Vec<usize>,
-    pub(crate) groups: Vec<(usize, usize)>,
+    pub(crate) groups: Vec<Range<usize>>,
     pub(crate) num_selectors: usize,
 }
 
@@ -32,27 +34,51 @@ pub(crate) fn selector_polynomials<F: RichField + Extendable<D>, const D: usize>
     max_degree: usize,
 ) -> (Vec<PolynomialValues<F>>, SelectorsInfo) {
     let n = instances.len();
+    let num_gates = gates.len();
+    let max_gate_degree = gates.last().expect("No gates?").0.degree();
+
+    let index = |id| gates.iter().position(|g| g.0.id() == id).unwrap();
+
+    // Special case if we can use only one selector polynomial.
+    if max_gate_degree + num_gates - 1 <= max_degree {
+        return (
+            vec![PolynomialValues::new(
+                instances
+                    .iter()
+                    .map(|g| F::from_canonical_usize(index(g.gate_ref.0.id())))
+                    .collect(),
+            )],
+            SelectorsInfo {
+                selector_indices: vec![0; num_gates],
+                groups: vec![0..num_gates],
+                num_selectors: 1,
+            },
+        );
+    }
+
+    if max_gate_degree >= max_degree {
+        panic!(
+            "{} has too high degree. Consider increasing `quotient_degree_factor`.",
+            gates.last().unwrap().0.id()
+        );
+    }
 
     // Greedily construct the groups.
     let mut groups = Vec::new();
-    let mut pos = 0;
-    while pos < gates.len() {
-        let mut i = 0;
-        while (pos + i < gates.len()) && (i + gates[pos + i].0.degree() < max_degree) {
-            i += 1;
+    let mut start = 0;
+    while start < num_gates {
+        let mut size = 0;
+        while (start + size < gates.len()) && (size + gates[start + size].0.degree() < max_degree) {
+            size += 1;
         }
-        groups.push((pos, pos + i));
-        pos += i;
+        groups.push(start..start + size);
+        start += size;
     }
 
-    let index = |id| gates.iter().position(|g| g.0.id() == id).unwrap();
-    let group = |i| groups.iter().position(|&(a, b)| a <= i && i < b).unwrap();
+    let group = |i| groups.iter().position(|range| range.contains(&i)).unwrap();
 
     // `selector_indices[i] = j` iff the `i`-th gate uses the `j`-th selector polynomial.
-    let selector_indices = gates
-        .iter()
-        .map(|g| group(index(g.0.id())))
-        .collect::<Vec<_>>();
+    let selector_indices = (0..num_gates).map(group).collect();
 
     // Placeholder value to indicate that a gate doesn't use a selector polynomial.
     let unused = F::from_canonical_usize(UNUSED_SELECTOR);
diff --git a/plonky2/src/plonk/circuit_builder.rs b/plonky2/src/plonk/circuit_builder.rs
index 12180600..022e2b12 100644
--- a/plonky2/src/plonk/circuit_builder.rs
+++ b/plonky2/src/plonk/circuit_builder.rs
@@ -666,6 +666,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
 
         let quotient_degree_factor = self.config.max_quotient_degree_factor;
         let mut gates = self.gates.iter().cloned().collect::<Vec<_>>();
+        // Gates need to be sorted by their degrees to compute the selector polynomials.
         gates.sort_unstable_by_key(|g| (g.0.degree(), g.0.id()));
         let (mut constant_vecs, selectors_info) =
             selector_polynomials(&gates, &self.gate_instances, quotient_degree_factor + 1);
diff --git a/plonky2/src/plonk/vanishing_poly.rs b/plonky2/src/plonk/vanishing_poly.rs
index 4ee797a5..54a5fe98 100644
--- a/plonky2/src/plonk/vanishing_poly.rs
+++ b/plonky2/src/plonk/vanishing_poly.rs
@@ -220,7 +220,7 @@ pub fn evaluate_gate_constraints<
             vars,
             i,
             selector_index,
-            common_data.selectors_info.groups[selector_index],
+            common_data.selectors_info.groups[selector_index].clone(),
             common_data.selectors_info.num_selectors,
         );
         for (i, c) in gate_constraints.into_iter().enumerate() {
@@ -254,7 +254,7 @@ pub fn evaluate_gate_constraints_base_batch<
             vars_batch,
             i,
             selector_index,
-            common_data.selectors_info.groups[selector_index],
+            common_data.selectors_info.groups[selector_index].clone(),
             common_data.selectors_info.num_selectors,
         );
         debug_assert!(
@@ -290,7 +290,7 @@ pub fn evaluate_gate_constraints_recursively<
                 vars,
                 i,
                 selector_index,
-                common_data.selectors_info.groups[selector_index],
+                common_data.selectors_info.groups[selector_index].clone(),
                 common_data.selectors_info.num_selectors,
                 &mut all_gate_constraints,
             )