diff --git a/plonky2/src/fri/mod.rs b/plonky2/src/fri/mod.rs
index c491f8f0..4ed2ea3b 100644
--- a/plonky2/src/fri/mod.rs
+++ b/plonky2/src/fri/mod.rs
@@ -35,6 +35,7 @@ impl FriConfig {
         let reduction_arity_bits = self.reduction_strategy.reduction_arity_bits(
             degree_bits,
             self.rate_bits,
+            self.cap_height,
             self.num_query_rounds,
         );
         FriParams {
@@ -67,7 +68,7 @@ pub struct FriParams {
 }
 
 impl FriParams {
-    pub(crate) fn total_arities(&self) -> usize {
+    pub fn total_arities(&self) -> usize {
         self.reduction_arity_bits.iter().sum()
     }
 
diff --git a/plonky2/src/fri/reduction_strategies.rs b/plonky2/src/fri/reduction_strategies.rs
index 49eda3ba..4252564e 100644
--- a/plonky2/src/fri/reduction_strategies.rs
+++ b/plonky2/src/fri/reduction_strategies.rs
@@ -9,9 +9,10 @@ pub enum FriReductionStrategy {
     Fixed(Vec<usize>),
 
     /// `ConstantArityBits(arity_bits, final_poly_bits)` applies reductions of arity `2^arity_bits`
-    /// until the polynomial degree is `2^final_poly_bits` or less. This tends to work well in the
-    /// recursive setting, as it avoids needing multiple configurations of gates used in FRI
-    /// verification, such as `InterpolationGate`.
+    /// until the polynomial degree is less than or equal to `2^final_poly_bits` or until any further
+    /// `arity_bits`-reduction makes the last FRI tree have height less than `cap_height`.
+    /// This tends to work well in the recursive setting, as it avoids needing multiple configurations
+    /// of gates used in FRI verification, such as `InterpolationGate`.
     ConstantArityBits(usize, usize),
 
     /// `MinSize(opt_max_arity_bits)` searches for an optimal sequence of reduction arities, with an
@@ -26,17 +27,20 @@ impl FriReductionStrategy {
         &self,
         mut degree_bits: usize,
         rate_bits: usize,
+        cap_height: usize,
         num_queries: usize,
     ) -> Vec<usize> {
         match self {
             FriReductionStrategy::Fixed(reduction_arity_bits) => reduction_arity_bits.to_vec(),
 
-            FriReductionStrategy::ConstantArityBits(arity_bits, final_poly_bits) => {
+            &FriReductionStrategy::ConstantArityBits(arity_bits, final_poly_bits) => {
                 let mut result = Vec::new();
-                while degree_bits > *final_poly_bits {
-                    result.push(*arity_bits);
-                    assert!(degree_bits >= *arity_bits);
-                    degree_bits -= *arity_bits;
+                while degree_bits > final_poly_bits
+                    && degree_bits + rate_bits - arity_bits >= cap_height
+                {
+                    result.push(arity_bits);
+                    assert!(degree_bits >= arity_bits);
+                    degree_bits -= arity_bits;
                 }
                 result.shrink_to_fit();
                 result
diff --git a/plonky2/src/plonk/circuit_builder.rs b/plonky2/src/plonk/circuit_builder.rs
index bd216389..8e2f2e10 100644
--- a/plonky2/src/plonk/circuit_builder.rs
+++ b/plonky2/src/plonk/circuit_builder.rs
@@ -639,6 +639,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         let mut timing = TimingTree::new("preprocess", Level::Trace);
         let start = Instant::now();
         let rate_bits = self.config.fri_config.rate_bits;
+        let cap_height = self.config.fri_config.cap_height;
 
         // Hash the public inputs, and route them to a `PublicInputGate` which will enforce that
         // those hash wires match the claimed public inputs.
@@ -664,7 +665,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         let degree_bits = log2_strict(degree);
         let fri_params = self.fri_params(degree_bits);
         assert!(
-            fri_params.total_arities() <= degree_bits,
+            fri_params.total_arities() <= degree_bits + rate_bits - cap_height,
             "FRI total reduction arity is too large.",
         );
 
@@ -705,7 +706,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
             constants_sigmas_vecs,
             rate_bits,
             PlonkOracle::CONSTANTS_SIGMAS.blinding,
-            self.config.fri_config.cap_height,
+            cap_height,
             &mut timing,
             Some(&fft_root_table),
         );
diff --git a/starky/src/prover.rs b/starky/src/prover.rs
index 3c067306..be1f198b 100644
--- a/starky/src/prover.rs
+++ b/starky/src/prover.rs
@@ -40,6 +40,13 @@ where
 {
     let degree = trace.len();
     let degree_bits = log2_strict(degree);
+    let fri_params = config.fri_params(degree_bits);
+    let rate_bits = config.fri_config.rate_bits;
+    let cap_height = config.fri_config.cap_height;
+    assert!(
+        fri_params.total_arities() <= degree_bits + rate_bits - cap_height,
+        "FRI total reduction arity is too large.",
+    );
 
     let trace_vecs = trace.iter().map(|row| row.to_vec()).collect_vec();
     let trace_col_major: Vec<Vec<F>> = transpose(&trace_vecs);
@@ -53,8 +60,6 @@ where
             .collect()
     );
 
-    let rate_bits = config.fri_config.rate_bits;
-    let cap_height = config.fri_config.cap_height;
     let trace_commitment = timed!(
         timing,
         "compute trace commitment",
@@ -160,7 +165,6 @@ where
         .chain(permutation_zs_commitment.as_ref())
         .chain(once(&quotient_commitment))
         .collect_vec();
-    let fri_params = config.fri_params(degree_bits);
 
     let opening_proof = timed!(
         timing,