diff --git a/src/circuit_builder.rs b/src/circuit_builder.rs
index 93b440ab..f1db3ae3 100644
--- a/src/circuit_builder.rs
+++ b/src/circuit_builder.rs
@@ -403,6 +403,7 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
 
         let gates = self.gates.iter().cloned().collect();
         let (gate_tree, max_filtered_constraint_degree, num_constants) = Tree::from_gates(gates);
+        let max_filtered_constraint_degree = max_filtered_constraint_degree.max(3);
         let prefixed_gates = PrefixedGate::from_tree(gate_tree);
 
         let degree_bits = log2_strict(degree);
diff --git a/src/util/partial_products.rs b/src/util/partial_products.rs
index e7c9069b..c3e5c2cd 100644
--- a/src/util/partial_products.rs
+++ b/src/util/partial_products.rs
@@ -25,6 +25,7 @@ pub fn partial_products<T: Product + Copy>(v: &[T], max_degree: usize) -> Vec<T>
 /// Returns a tuple `(a,b)`, where `a` is the length of the output of `partial_products()` on a
 /// vector of length `n`, and `b` is the number of elements needed to compute the final product.
 pub fn num_partial_products(n: usize, max_degree: usize) -> (usize, usize) {
+    debug_assert!(max_degree > 1);
     let mut res = 0;
     let mut remainder = n;
     while remainder > max_degree {