diff --git a/src/ipa_pc/mod.rs b/src/ipa_pc/mod.rs
index e069fee2..0fd249e7 100644
--- a/src/ipa_pc/mod.rs
+++ b/src/ipa_pc/mod.rs
@@ -187,9 +187,7 @@ impl<G: AffineCurve, D: Digest> InnerProductArgPC<G, D> {
         supported_degree: usize,
         p: &LabeledPolynomial<G::ScalarField>,
     ) -> Result<(), Error> {
-        if p.degree() < 1 {
-            return Err(Error::DegreeIsZero);
-        } else if p.degree() > supported_degree {
+        if p.degree() > supported_degree {
             return Err(Error::TooManyCoefficients {
                 num_coefficients: p.degree() + 1,
                 num_powers: supported_degree + 1,
@@ -1085,6 +1083,12 @@ mod tests {
     type PC<E, D> = InnerProductArgPC<E, D>;
     type PC_DEE = PC<Affine, Blake2s>;
 
+    #[test]
+    fn constant_poly_test() {
+        use crate::tests::*;
+        constant_poly_test::<_, PC_DEE>().expect("test failed for tweedle_dee-blake2s");
+    }
+
     #[test]
     fn single_poly_test() {
         use crate::tests::*;
diff --git a/src/lib.rs b/src/lib.rs
index ada1881b..983f6718 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -755,8 +755,11 @@ pub mod tests {
         let pp = PC::setup(max_degree, rng)?;
 
         for _ in 0..num_iters {
-            let supported_degree = supported_degree
-                .unwrap_or(rand::distributions::Uniform::from(1..=max_degree).sample(rng));
+            let supported_degree = match supported_degree {
+                Some(0) => 0,
+                Some(d) => d,
+                None => rand::distributions::Uniform::from(1..=max_degree).sample(rng)
+            };
             assert!(
                 max_degree >= supported_degree,
                 "max_degree < supported_degree"
@@ -777,7 +780,11 @@ pub mod tests {
             for i in 0..num_polynomials {
                 let label = format!("Test{}", i);
                 labels.push(label.clone());
-                let degree = rand::distributions::Uniform::from(1..=supported_degree).sample(rng);
+                let degree = if supported_degree > 0 {
+                    rand::distributions::Uniform::from(1..=supported_degree).sample(rng)
+                } else {
+                    0
+                };
                 let poly = Polynomial::rand(degree, rng);
 
                 let degree_bound = if let Some(degree_bounds) = &mut degree_bounds {
@@ -1042,6 +1049,23 @@ pub mod tests {
         Ok(())
     }
 
+    pub fn constant_poly_test<F, PC>() -> Result<(), PC::Error>
+        where
+            F: Field,
+            PC: PolynomialCommitment<F>,
+    {
+        let info = TestInfo {
+            num_iters: 100,
+            max_degree: None,
+            supported_degree: Some(0),
+            num_polynomials: 1,
+            enforce_degree_bounds: false,
+            max_num_queries: 1,
+            ..Default::default()
+        };
+        test_template::<F, PC>(info)
+    }
+
     pub fn single_poly_test<F, PC>() -> Result<(), PC::Error>
     where
         F: Field,