diff --git a/src/plonk/circuit.rs b/src/plonk/circuit.rs
index e6b71b1..eab4517 100644
--- a/src/plonk/circuit.rs
+++ b/src/plonk/circuit.rs
@@ -1,6 +1,6 @@
 use core::cmp::max;
 use core::ops::{Add, Mul};
-use std::collections::HashMap;
+use std::collections::BTreeMap;
 
 use super::Error;
 use crate::arithmetic::Field;
@@ -160,7 +160,7 @@ pub struct MetaCircuit<F> {
     pub(crate) fixed_queries: Vec<(FixedWire, Rotation)>,
 
     // Mapping from a witness vector rotation to the index in the point vector.
-    pub(crate) rotations: HashMap<Rotation, PointIndex>,
+    pub(crate) rotations: BTreeMap<Rotation, PointIndex>,
 
     // Vector of permutation arguments, where each corresponds to a set of wires
     // that are involved in a permutation argument. As an example, we could have
@@ -174,7 +174,7 @@ pub struct MetaCircuit<F> {
 
 impl<F: Field> Default for MetaCircuit<F> {
     fn default() -> MetaCircuit<F> {
-        let mut rotations = HashMap::new();
+        let mut rotations = BTreeMap::new();
         rotations.insert(Rotation::default(), PointIndex(0));
 
         MetaCircuit {
@@ -195,9 +195,9 @@ impl<F: Field> MetaCircuit<F> {
     pub fn permutation(&mut self, wires: &[AdviceWire]) -> usize {
         let index = self.permutations.len();
         if index == 0 {
-            // no permutations
-            let point_idx = self.rotations.len();
-            self.rotations.insert(Rotation(-1), PointIndex(point_idx));
+            let at = Rotation(-1);
+            let len = self.rotations.len();
+            self.rotations.entry(at).or_insert(PointIndex(len));
         }
         self.permutations.push(wires.to_vec());
 
diff --git a/src/plonk/domain.rs b/src/plonk/domain.rs
index 62ec88d..81b74b6 100644
--- a/src/plonk/domain.rs
+++ b/src/plonk/domain.rs
@@ -2,7 +2,7 @@ use crate::arithmetic::{best_fft, parallelize, Field, Group};
 
 /// Describes a relative location in the evaluation domain; applying a rotation
 /// by i will rotate the vector in the evaluation domain by i.
-#[derive(Copy, Clone, Debug, Hash, PartialEq, Eq)]
+#[derive(Copy, Clone, Debug, Hash, PartialEq, Eq, Ord, PartialOrd)]
 pub struct Rotation(pub i32);
 
 impl Default for Rotation {
diff --git a/src/plonk/prover.rs b/src/plonk/prover.rs
index 861fa8c..03939fd 100644
--- a/src/plonk/prover.rs
+++ b/src/plonk/prover.rs
@@ -562,13 +562,11 @@ impl<C: CurveAffine> Proof<C> {
 
         let x_6: C::Scalar = get_challenge_scalar(Challenge(transcript.squeeze().get_lower_128()));
 
-        let mut q_evals = vec![];
+        let mut q_evals = vec![C::Scalar::zero(); meta.rotations.len()];
 
         for (_, &point_index) in meta.rotations.iter() {
-            q_evals.push(eval_polynomial(
-                &q_polys[point_index.0].as_ref().unwrap(),
-                x_6,
-            ));
+            q_evals[point_index.0] =
+                eval_polynomial(&q_polys[point_index.0].as_ref().unwrap(), x_6);
         }
 
         for eval in q_evals.iter() {