diff --git a/src/gadgets/split_join.rs b/src/gadgets/split_join.rs
index dddae0be..9b84ed76 100644
--- a/src/gadgets/split_join.rs
+++ b/src/gadgets/split_join.rs
@@ -5,7 +5,7 @@ use crate::iop::generator::{GeneratedValues, SimpleGenerator};
 use crate::iop::target::{BoolTarget, Target};
 use crate::iop::witness::{PartitionWitness, Witness};
 use crate::plonk::circuit_builder::CircuitBuilder;
-use crate::util::ceil_div_usize;
+use crate::util::{bits_u64, ceil_div_usize};
 
 impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     /// Split the given integer into a list of wires, where each one represents a
@@ -16,7 +16,8 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         if num_bits == 0 {
             return Vec::new();
         }
-        let bits_per_gate = self.config.num_routed_wires - BaseSumGate::<2>::START_LIMBS;
+        let bits_per_gate = (bits_u64(F::ORDER) - 1)
+            .min(self.config.num_routed_wires - BaseSumGate::<2>::START_LIMBS);
         let k = ceil_div_usize(num_bits, bits_per_gate);
         let gates = (0..k)
             .map(|_| self.add_gate(BaseSumGate::<2>::new(bits_per_gate), vec![]))
diff --git a/src/gates/comparison.rs b/src/gates/comparison.rs
index 1a472550..0715b066 100644
--- a/src/gates/comparison.rs
+++ b/src/gates/comparison.rs
@@ -11,7 +11,7 @@ use crate::iop::witness::{PartitionWitness, Witness};
 use crate::plonk::circuit_builder::CircuitBuilder;
 use crate::plonk::plonk_common::{reduce_with_powers, reduce_with_powers_ext_recursive};
 use crate::plonk::vars::{EvaluationTargets, EvaluationVars, EvaluationVarsBase};
-use crate::util::ceil_div_usize;
+use crate::util::{bits_u64, ceil_div_usize};
 
 /// A gate for checking that one value is less than or equal to another.
 #[derive(Clone, Debug)]
@@ -23,6 +23,7 @@ pub struct ComparisonGate<F: PrimeField + Extendable<D>, const D: usize> {
 
 impl<F: RichField + Extendable<D>, const D: usize> ComparisonGate<F, D> {
     pub fn new(num_bits: usize, num_chunks: usize) -> Self {
+        debug_assert!(num_bits < bits_u64(F::ORDER));
         Self {
             num_bits,
             num_chunks,