diff --git a/w3f-plonk-common/src/domain.rs b/w3f-plonk-common/src/domain.rs
index a096cd9..07c12de 100644
--- a/w3f-plonk-common/src/domain.rs
+++ b/w3f-plonk-common/src/domain.rs
@@ -1,11 +1,11 @@
+use crate::FieldColumn;
 use ark_ff::{batch_inversion, FftField, Zero};
 use ark_poly::univariate::DensePolynomial;
 use ark_poly::{
     DenseUVPolynomial, EvaluationDomain, Evaluations, GeneralEvaluationDomain, Polynomial,
 };
 use ark_std::{vec, vec::Vec};
-
-use crate::FieldColumn;
+use getrandom_or_panic::getrandom_or_panic;
 
 pub const ZK_ROWS: usize = 3;
 
@@ -25,26 +25,28 @@ impl<F: FftField> Domains<F> {
         Self { x1, x4 }
     }
 
-    fn column_from_evals(&self, evals: Vec<F>, len: usize) -> FieldColumn<F> {
+    fn column_from_evals(&self, evals: Vec<F>, constrained_len: usize) -> FieldColumn<F> {
         assert_eq!(evals.len(), self.x1.size());
+        assert!(constrained_len <= evals.len());
         let evals = Evaluations::from_vec_and_domain(evals, self.x1);
         let poly = evals.interpolate_by_ref();
         let evals_4x = poly.evaluate_over_domain_by_ref(self.x4);
         FieldColumn {
-            len,
+            constrained_len,
             poly,
             evals,
             evals_4x,
         }
     }
 
-    fn column_from_poly(&self, poly: DensePolynomial<F>, len: usize) -> FieldColumn<F> {
+    fn column_from_poly(&self, poly: DensePolynomial<F>, constrained_len: usize) -> FieldColumn<F> {
         assert!(poly.degree() < self.x1.size());
+        assert!(constrained_len <= self.x1.size());
         let evals_4x = self.amplify(&poly);
         let evals = evals_4x.evals.iter().step_by(4).cloned().collect();
         let evals = Evaluations::from_vec_and_domain(evals, self.x1);
         FieldColumn {
-            len,
+            constrained_len,
             poly,
             evals,
             evals_4x,
@@ -111,9 +113,10 @@ impl<F: FftField> Domain<F> {
         assert!(len <= self.capacity);
         if self.hiding && hidden && !cfg!(feature = "test-vectors") {
             evals.resize(self.capacity, F::zero());
-            evals.resize_with(self.domains.x1.size(), || {
-                F::rand(&mut getrandom_or_panic::getrandom_or_panic())
-            });
+            evals.resize_with(
+                self.domains.x1.size(),
+                || F::rand(&mut getrandom_or_panic()),
+            );
         } else {
             evals.resize(self.domains.x1.size(), F::zero());
         }
diff --git a/w3f-plonk-common/src/gadgets/booleanity.rs b/w3f-plonk-common/src/gadgets/booleanity.rs
index ace75da..9f9aab3 100644
--- a/w3f-plonk-common/src/gadgets/booleanity.rs
+++ b/w3f-plonk-common/src/gadgets/booleanity.rs
@@ -26,6 +26,8 @@ impl<F: FftField> BitColumn<F> {
 }
 
 impl<F: FftField> Column<F> for BitColumn<F> {
+    type T = bool;
+
     fn domain(&self) -> GeneralEvaluationDomain<F> {
         self.col.domain()
     }
@@ -34,8 +36,18 @@ impl<F: FftField> Column<F> for BitColumn<F> {
         self.col.domain_4x()
     }
 
-    fn as_poly(&self) -> &DensePolynomial<F> {
-        self.col.as_poly()
+    fn constrained_len(&self) -> usize {
+        self.col.constrained_len()
+    }
+
+    fn constrained_vals(&self) -> &[Self::T] {
+        &self.bits[0..self.constrained_len()]
+    }
+}
+
+impl<F: FftField> BitColumn<F> {
+    pub fn evaluate(&self, z: &F) -> F {
+        self.col.evaluate(z)
     }
 }
 
diff --git a/w3f-plonk-common/src/gadgets/column_sum.rs b/w3f-plonk-common/src/gadgets/column_sum.rs
index 0e841ec..83a177f 100644
--- a/w3f-plonk-common/src/gadgets/column_sum.rs
+++ b/w3f-plonk-common/src/gadgets/column_sum.rs
@@ -35,8 +35,8 @@ pub struct ColumnSumEvals<F: Field> {
 
 impl<F: FftField> ColumnSumPolys<F> {
     pub fn init(col: FieldColumn<F>, domain: &Domain<F>) -> Self {
-        assert_eq!(col.len, domain.capacity - 1); // last element is not constrained
-        let partial_sums = Self::partial_sums(col.vals());
+        assert_eq!(col.constrained_len(), domain.capacity - 1); // last element is not constrained
+        let partial_sums = Self::partial_sums(col.constrained_vals());
         let mut acc = vec![F::zero()];
         acc.extend(partial_sums);
         let acc = domain.private_column(acc);
diff --git a/w3f-plonk-common/src/gadgets/ec/mod.rs b/w3f-plonk-common/src/gadgets/ec/mod.rs
index 048548c..e39b65b 100644
--- a/w3f-plonk-common/src/gadgets/ec/mod.rs
+++ b/w3f-plonk-common/src/gadgets/ec/mod.rs
@@ -3,7 +3,7 @@ use crate::gadgets::booleanity::BitColumn;
 use crate::{Column, FieldColumn};
 use ark_ec::{AffineRepr, CurveGroup};
 use ark_ff::{FftField, Field};
-
+use ark_poly::GeneralEvaluationDomain;
 // use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::marker::PhantomData;
 use ark_std::vec::Vec;
@@ -31,6 +31,7 @@ impl<F: FftField, P: AffineRepr<BaseField = F>> AffineColumn<F, P> {
         let ys = domain.column(ys, hidden);
         Self { points, xs, ys }
     }
+
     pub fn private_column(points: Vec<P>, domain: &Domain<F>) -> Self {
         Self::column(points, domain, true)
     }
@@ -42,6 +43,32 @@ impl<F: FftField, P: AffineRepr<BaseField = F>> AffineColumn<F, P> {
     pub fn evaluate(&self, z: &F) -> (F, F) {
         (self.xs.evaluate(z), self.ys.evaluate(z))
     }
+
+    pub fn trim_to(&mut self, n: usize) {
+        assert!(n <= self.constrained_len());
+        self.xs.constrained_len = n;
+        self.ys.constrained_len = n;
+    }
+}
+
+impl<F: FftField, P: AffineRepr<BaseField = F>> Column<F> for AffineColumn<F, P> {
+    type T = P;
+
+    fn domain(&self) -> GeneralEvaluationDomain<F> {
+        self.xs.domain()
+    }
+
+    fn domain_4x(&self) -> GeneralEvaluationDomain<F> {
+        self.xs.domain_4x()
+    }
+
+    fn constrained_len(&self) -> usize {
+        self.xs.constrained_len()
+    }
+
+    fn constrained_vals(&self) -> &[Self::T] {
+        &self.points[0..self.constrained_len()]
+    }
 }
 
 // Conditional affine addition:
@@ -71,13 +98,13 @@ where
         seed: P,
         domain: &Domain<F>,
     ) -> Self {
-        assert_eq!(bitmask.bits.len(), domain.capacity - 1);
-        // assert_eq!(points.points.len(), domain.capacity - 1); //TODO
+        assert_eq!(bitmask.constrained_len(), domain.capacity - 1);
+        assert_eq!(points.constrained_len(), domain.capacity - 1);
         let not_last = domain.not_last_row.clone();
         let acc = bitmask
-            .bits
+            .constrained_vals()
             .iter()
-            .zip(points.points.iter())
+            .zip(points.constrained_vals())
             .scan(seed, |acc, (&b, point)| {
                 if b {
                     *acc = (*acc + point).into_affine();
diff --git a/w3f-plonk-common/src/gadgets/ec/te_doubling.rs b/w3f-plonk-common/src/gadgets/ec/te_doubling.rs
index fe893cd..2892511 100644
--- a/w3f-plonk-common/src/gadgets/ec/te_doubling.rs
+++ b/w3f-plonk-common/src/gadgets/ec/te_doubling.rs
@@ -29,7 +29,7 @@ where
     F: FftField,
 {
     pub fn init(p: P, domain: &Domain<F>) -> Self {
-        let doublings = Self::doublings_of(p, domain);
+        let doublings = Self::doublings_of(p, domain.capacity);
         let doublings = AffineColumn::public_column(doublings, domain);
         let not_last = domain.not_last_row.clone();
         Self {
@@ -38,11 +38,11 @@ where
         }
     }
 
-    pub fn doublings_of(p: P, domain: &Domain<F>) -> Vec<P> {
+    pub fn doublings_of(p: P, n: usize) -> Vec<P> {
         let mut p = p.into_group();
-        let mut doublings = Vec::with_capacity(domain.capacity);
+        let mut doublings = Vec::with_capacity(n);
         doublings.push(p);
-        for _ in 1..domain.capacity {
+        for _ in 1..n {
             p.double_in_place();
             doublings.push(p);
         }
diff --git a/w3f-plonk-common/src/gadgets/fixed_cells.rs b/w3f-plonk-common/src/gadgets/fixed_cells.rs
index 56a9fd8..72883cb 100644
--- a/w3f-plonk-common/src/gadgets/fixed_cells.rs
+++ b/w3f-plonk-common/src/gadgets/fixed_cells.rs
@@ -24,7 +24,7 @@ pub struct FixedCellsValues<F: Field> {
 
 impl<F: FftField> FixedCells<F> {
     pub fn init(col: FieldColumn<F>, domain: &Domain<F>) -> Self {
-        assert_eq!(col.len, domain.capacity);
+        assert_eq!(col.constrained_len, domain.capacity);
         let l_first = domain.l_first.clone();
         let l_last = domain.l_last.clone();
         Self {
@@ -35,7 +35,7 @@ impl<F: FftField> FixedCells<F> {
     }
 
     pub fn constraints(&self) -> Vec<Evaluations<F>> {
-        let domain_capacity = self.col.len; // that's an ugly way to learn the capacity, but we've asserted it above.
+        let domain_capacity = self.col.constrained_len; // that's an ugly way to learn the capacity, but we've asserted it above.
         let c = &Self::constraint_cell(&self.col, &self.l_first, 0)
             + &Self::constraint_cell(&self.col, &self.l_last, domain_capacity - 1);
         vec![c]
diff --git a/w3f-plonk-common/src/gadgets/inner_prod.rs b/w3f-plonk-common/src/gadgets/inner_prod.rs
index f977912..54df870 100644
--- a/w3f-plonk-common/src/gadgets/inner_prod.rs
+++ b/w3f-plonk-common/src/gadgets/inner_prod.rs
@@ -24,9 +24,9 @@ pub struct InnerProdValues<F: Field> {
 
 impl<F: FftField> InnerProd<F> {
     pub fn init(a: FieldColumn<F>, b: FieldColumn<F>, domain: &Domain<F>) -> Self {
-        assert_eq!(a.len, domain.capacity - 1); // last element is not constrained
-        assert_eq!(b.len, domain.capacity - 1); // last element is not constrained
-        let inner_prods = Self::partial_inner_prods(a.vals(), b.vals());
+        assert_eq!(a.constrained_len(), domain.capacity - 1); // last element is not constrained
+        assert_eq!(b.constrained_len(), domain.capacity - 1); // last element is not constrained
+        let inner_prods = Self::partial_inner_prods(a.constrained_vals(), b.constrained_vals());
         let mut acc = vec![F::zero()];
         acc.extend(inner_prods);
         let acc = domain.private_column(acc);
diff --git a/w3f-plonk-common/src/lib.rs b/w3f-plonk-common/src/lib.rs
index 87208d9..7194442 100644
--- a/w3f-plonk-common/src/lib.rs
+++ b/w3f-plonk-common/src/lib.rs
@@ -16,22 +16,24 @@ pub mod transcript;
 pub mod verifier;
 
 pub trait Column<F: FftField> {
+    /// Type of a column cell.
+    type T;
+    /// Evaluation domain of the associated column polynomial `p`:
+    /// `p(w^i) = col[i]` for the domain generator `w`.
     fn domain(&self) -> GeneralEvaluationDomain<F>;
+    /// Evaluation domain of constraint polynomials.
     fn domain_4x(&self) -> GeneralEvaluationDomain<F>;
-    fn as_poly(&self) -> &DensePolynomial<F>;
-    fn size(&self) -> usize {
-        self.domain().size()
-    }
-    fn evaluate(&self, z: &F) -> F {
-        self.as_poly().evaluate(z)
-    }
+    /// Length of the constrained prefix of the column.
+    /// Is either equal to `domain.capacity` or `domain.capacity - 1`.
+    fn constrained_len(&self) -> usize;
+    /// Values of the cells that are constrained.
+    fn constrained_vals(&self) -> &[Self::T];
 }
 
 // #[derive(Clone, CanonicalSerialize, CanonicalDeserialize)]
 #[derive(Clone)]
 pub struct FieldColumn<F: FftField> {
-    // actual (constrained) len of the input in evaluation form
-    pub len: usize,
+    constrained_len: usize,
     pub poly: DensePolynomial<F>,
     pub evals: Evaluations<F>,
     pub evals_4x: Evaluations<F>,
@@ -44,12 +46,18 @@ impl<F: FftField> FieldColumn<F> {
         Evaluations::from_vec_and_domain(evals_4x, self.domain_4x())
     }
 
-    pub fn vals(&self) -> &[F] {
-        &self.evals.evals[..self.len]
+    pub fn as_poly(&self) -> &DensePolynomial<F> {
+        &self.poly
+    }
+
+    pub fn evaluate(&self, z: &F) -> F {
+        self.poly.evaluate(z)
     }
 }
 
 impl<F: FftField> Column<F> for FieldColumn<F> {
+    type T = F;
+
     fn domain(&self) -> GeneralEvaluationDomain<F> {
         self.evals.domain()
     }
@@ -58,8 +66,12 @@ impl<F: FftField> Column<F> for FieldColumn<F> {
         self.evals_4x.domain()
     }
 
-    fn as_poly(&self) -> &DensePolynomial<F> {
-        &self.poly
+    fn constrained_len(&self) -> usize {
+        self.constrained_len
+    }
+
+    fn constrained_vals(&self) -> &[Self::T] {
+        &self.evals.evals[..self.constrained_len]
     }
 }
 
diff --git a/w3f-ring-proof/src/piop/mod.rs b/w3f-ring-proof/src/piop/mod.rs
index a4d2c71..85976b1 100644
--- a/w3f-ring-proof/src/piop/mod.rs
+++ b/w3f-ring-proof/src/piop/mod.rs
@@ -13,7 +13,7 @@ use w3f_pcs::pcs::{Commitment, PcsParams, PCS};
 pub(crate) use prover::PiopProver;
 pub(crate) use verifier::PiopVerifier;
 use w3f_plonk_common::gadgets::ec::AffineColumn;
-use w3f_plonk_common::{Column, ColumnsCommited, ColumnsEvaluated, FieldColumn};
+use w3f_plonk_common::{ColumnsCommited, ColumnsEvaluated, FieldColumn};
 
 use crate::ring::Ring;
 use crate::PiopParams;
diff --git a/w3f-ring-proof/src/piop/prover.rs b/w3f-ring-proof/src/piop/prover.rs
index 07267c3..bba9c46 100644
--- a/w3f-ring-proof/src/piop/prover.rs
+++ b/w3f-ring-proof/src/piop/prover.rs
@@ -18,7 +18,7 @@ use w3f_plonk_common::gadgets::fixed_cells::FixedCells;
 use w3f_plonk_common::gadgets::inner_prod::InnerProd;
 use w3f_plonk_common::gadgets::ProverGadget;
 use w3f_plonk_common::piop::ProverPiop;
-use w3f_plonk_common::{Column, FieldColumn};
+use w3f_plonk_common::FieldColumn;
 
 // The 'table': columns representing the execution trace of the computation
 // and the constraints -- polynomials that vanish on every 2 consecutive rows.
@@ -100,7 +100,7 @@ where
         &self,
         commit: Fun,
     ) -> Self::Commitments {
-        let bits = commit(self.bits.as_poly());
+        let bits = commit(self.bits.col.as_poly());
         let cond_add_acc = [
             commit(self.cond_add.acc.xs.as_poly()),
             commit(self.cond_add.acc.ys.as_poly()),
@@ -121,7 +121,7 @@ where
             self.points.xs.as_poly().clone(),
             self.points.ys.as_poly().clone(),
             self.ring_selector.as_poly().clone(),
-            self.bits.as_poly().clone(),
+            self.bits.col.as_poly().clone(),
             self.inner_prod.acc.as_poly().clone(),
             self.cond_add.acc.xs.as_poly().clone(),
             self.cond_add.acc.ys.as_poly().clone(),
diff --git a/w3f-ring-vrf-snark/src/piop/cell_equality.rs b/w3f-ring-vrf-snark/src/piop/cell_equality.rs
index 0e2f1c6..61e5fb6 100644
--- a/w3f-ring-vrf-snark/src/piop/cell_equality.rs
+++ b/w3f-ring-vrf-snark/src/piop/cell_equality.rs
@@ -6,7 +6,7 @@ use ark_std::{vec, vec::Vec};
 
 use w3f_plonk_common::domain::Domain;
 use w3f_plonk_common::gadgets::VerifierGadget;
-use w3f_plonk_common::FieldColumn;
+use w3f_plonk_common::{Column, FieldColumn};
 
 pub struct CellEqualityPolys<F: FftField> {
     a: FieldColumn<F>,
@@ -22,8 +22,8 @@ pub struct CellEqualityEvals<F: Field> {
 
 impl<F: FftField> CellEqualityPolys<F> {
     pub fn init(a: FieldColumn<F>, b: FieldColumn<F>, domain: &Domain<F>) -> Self {
-        assert_eq!(a.len, domain.capacity);
-        assert_eq!(b.len, domain.capacity);
+        assert_eq!(a.constrained_len(), domain.capacity);
+        assert_eq!(b.constrained_len(), domain.capacity);
         let a_last = a.evals.evals[domain.capacity - 1];
         let b_last = b.evals.evals[domain.capacity - 1];
         assert_eq!(a_last, b_last);
diff --git a/w3f-ring-vrf-snark/src/piop/mod.rs b/w3f-ring-vrf-snark/src/piop/mod.rs
index ca040cc..ff23210 100644
--- a/w3f-ring-vrf-snark/src/piop/mod.rs
+++ b/w3f-ring-vrf-snark/src/piop/mod.rs
@@ -13,7 +13,7 @@ use w3f_pcs::pcs::{Commitment, PcsParams, PCS};
 pub(crate) use prover::PiopProver;
 pub(crate) use verifier::PiopVerifier;
 use w3f_plonk_common::gadgets::ec::AffineColumn;
-use w3f_plonk_common::{Column, ColumnsCommited, ColumnsEvaluated};
+use w3f_plonk_common::{ColumnsCommited, ColumnsEvaluated};
 
 use crate::PiopParams;
 
diff --git a/w3f-ring-vrf-snark/src/piop/params.rs b/w3f-ring-vrf-snark/src/piop/params.rs
index c275b65..1f2af63 100644
--- a/w3f-ring-vrf-snark/src/piop/params.rs
+++ b/w3f-ring-vrf-snark/src/piop/params.rs
@@ -64,7 +64,7 @@ impl<F: PrimeField, Curve: TECurveConfig<BaseField = F>> PiopParams<F, Curve> {
     }
 
     fn doublings_of_g_col(&self) -> AffineColumn<F, Affine<Curve>> {
-        let doublings_of_g = Doubling::doublings_of(self.g, &self.domain);
+        let doublings_of_g = Doubling::doublings_of(self.g, &self.domain.capacity - 1);
         AffineColumn::public_column(doublings_of_g, &self.domain)
     }
 
diff --git a/w3f-ring-vrf-snark/src/piop/prover.rs b/w3f-ring-vrf-snark/src/piop/prover.rs
index cc73f17..b90e8ec 100644
--- a/w3f-ring-vrf-snark/src/piop/prover.rs
+++ b/w3f-ring-vrf-snark/src/piop/prover.rs
@@ -20,7 +20,6 @@ use w3f_plonk_common::piop::ProverPiop;
 use crate::piop::cell_equality::CellEqualityPolys;
 use w3f_plonk_common::gadgets::column_sum::ColumnSumPolys;
 use w3f_plonk_common::gadgets::ec::te_doubling::Doubling;
-use w3f_plonk_common::Column;
 
 /// The prover's private input is its secret key `sk`.
 /// The public inputs are:
@@ -117,7 +116,10 @@ impl<F: PrimeField, Curve: TECurveConfig<BaseField = F>> PiopProver<F, Curve> {
         );
 
         let doublings_of_in_gadget = Doubling::init(vrf_in, &domain);
-        let doublings_of_in = doublings_of_in_gadget.doublings.clone();
+        let mut doublings_of_in = doublings_of_in_gadget.doublings.clone();
+        // The `doublings` gadget constrains the points in the column up to `domain.capacity`,
+        // but the `additions` gadget can't constrain the last point (due to the `seed` point).
+        doublings_of_in.trim_to(domain.capacity - 1);
         let out_from_in = CondAdd::init(sk_bits.clone(), doublings_of_in, params.seed, &domain);
         let out_from_in_x = FixedCells::init(out_from_in.acc.xs.clone(), &domain);
         let out_from_in_y = FixedCells::init(out_from_in.acc.ys.clone(), &domain);
@@ -174,8 +176,8 @@ where
         &self,
         commit: Fun,
     ) -> Self::Commitments {
-        let sk_bits = commit(self.sk_bits.as_poly());
-        let pk_index = commit(self.pk_index.as_poly());
+        let sk_bits = commit(self.sk_bits.col.as_poly());
+        let pk_index = commit(self.pk_index.col.as_poly());
         let pk_from_sk = [
             commit(self.pk_from_sk.acc.xs.as_poly()),
             commit(self.pk_from_sk.acc.ys.as_poly()),
@@ -213,8 +215,8 @@ where
             self.pks.ys.as_poly().clone(),
             self.doublings_of_g.xs.as_poly().clone(),
             self.doublings_of_g.ys.as_poly().clone(),
-            self.sk_bits.as_poly().clone(),
-            self.pk_index.as_poly().clone(),
+            self.sk_bits.col.as_poly().clone(),
+            self.pk_index.col.as_poly().clone(),
             self.pk_from_sk.acc.xs.as_poly().clone(),
             self.pk_from_sk.acc.ys.as_poly().clone(),
             self.doublings_of_in_gadget.doublings.xs.as_poly().clone(),