diff --git a/examples/performance_model.rs b/examples/performance_model.rs
index 1138bc0..1d5d1d7 100644
--- a/examples/performance_model.rs
+++ b/examples/performance_model.rs
@@ -157,24 +157,11 @@ impl<'a, FF: FieldExt, CS: Assignment<FF>> StandardCS<FF> for StandardPLONK<'a,
         ))
     }
     fn copy(&mut self, left: Variable, right: Variable) -> Result<(), Error> {
-        let left_column = match left.0 {
-            x if x == self.config.a => 0,
-            x if x == self.config.b => 1,
-            x if x == self.config.c => 2,
-            _ => unreachable!(),
-        };
-        let right_column = match right.0 {
-            x if x == self.config.a => 0,
-            x if x == self.config.b => 1,
-            x if x == self.config.c => 2,
-            _ => unreachable!(),
-        };
-
         self.cs.copy(
             &self.config.perm,
-            left_column,
+            left.0.into(),
             left.1,
-            right_column,
+            right.0.into(),
             right.1,
         )
     }
diff --git a/src/circuit/layouter.rs b/src/circuit/layouter.rs
index 9561657..8ff687d 100644
--- a/src/circuit/layouter.rs
+++ b/src/circuit/layouter.rs
@@ -320,22 +320,11 @@ impl<'r, 'a, C: Chip, CS: Assignment<C::Field> + 'a> RegionLayouter<C>
         left: Cell,
         right: Cell,
     ) -> Result<(), Error> {
-        let left_column = permutation
-            .mapping()
-            .iter()
-            .position(|c| c == &left.column)
-            .ok_or(Error::SynthesisError)?;
-        let right_column = permutation
-            .mapping()
-            .iter()
-            .position(|c| c == &right.column)
-            .ok_or(Error::SynthesisError)?;
-
         self.layouter.cs.copy(
             permutation,
-            left_column,
+            left.column,
             *self.layouter.regions[*left.region_index] + left.row_offset,
-            right_column,
+            right.column,
             *self.layouter.regions[*right.region_index] + right.row_offset,
         )?;
 
diff --git a/src/dev.rs b/src/dev.rs
index f7fd500..f89a733 100644
--- a/src/dev.rs
+++ b/src/dev.rs
@@ -5,7 +5,7 @@ use ff::Field;
 use crate::{
     arithmetic::{FieldExt, Group},
     plonk::{
-        permutation, Advice, Assignment, Circuit, Column, ColumnType, ConstraintSystem, Error,
+        permutation, Advice, Any, Assignment, Circuit, Column, ColumnType, ConstraintSystem, Error,
         Expression, Fixed, Permutation,
     },
     poly::Rotation,
@@ -212,9 +212,9 @@ impl<F: Field + Group> Assignment<F> for MockProver<F> {
     fn copy(
         &mut self,
         permutation: &Permutation,
-        left_column: usize,
+        left_column: Column<Any>,
         left_row: usize,
-        right_column: usize,
+        right_column: Column<Any>,
         right_row: usize,
     ) -> Result<(), crate::plonk::Error> {
         // Check bounds first
@@ -222,7 +222,23 @@ impl<F: Field + Group> Assignment<F> for MockProver<F> {
             return Err(Error::BoundsFailure);
         }
 
-        self.permutations[permutation.index()].copy(left_column, left_row, right_column, right_row)
+        let left_column_index = permutation
+            .mapping()
+            .iter()
+            .position(|c| c == &left_column)
+            .ok_or(Error::SynthesisError)?;
+        let right_column_index = permutation
+            .mapping()
+            .iter()
+            .position(|c| c == &right_column)
+            .ok_or(Error::SynthesisError)?;
+
+        self.permutations[permutation.index()].copy(
+            left_column_index,
+            left_row,
+            right_column_index,
+            right_row,
+        )
     }
 
     fn push_namespace<NR, N>(&mut self, _: N)
diff --git a/src/plonk.rs b/src/plonk.rs
index 8199e38..f321fe2 100644
--- a/src/plonk.rs
+++ b/src/plonk.rs
@@ -380,31 +380,18 @@ fn test_proving() {
             ))
         }
         fn copy(&mut self, left: Variable, right: Variable) -> Result<(), Error> {
-            let left_column = match left.0 {
-                x if x == self.config.a => 0,
-                x if x == self.config.b => 1,
-                x if x == self.config.c => 2,
-                _ => unreachable!(),
-            };
-            let right_column = match right.0 {
-                x if x == self.config.a => 0,
-                x if x == self.config.b => 1,
-                x if x == self.config.c => 2,
-                _ => unreachable!(),
-            };
-
             self.cs.copy(
                 &self.config.perm,
-                left_column,
+                left.0.into(),
                 left.1,
-                right_column,
+                right.0.into(),
                 right.1,
             )?;
             self.cs.copy(
                 &self.config.perm2,
-                left_column,
+                left.0.into(),
                 left.1,
-                right_column,
+                right.0.into(),
                 right.1,
             )
         }
diff --git a/src/plonk/circuit.rs b/src/plonk/circuit.rs
index 85cef67..4893ddd 100644
--- a/src/plonk/circuit.rs
+++ b/src/plonk/circuit.rs
@@ -205,9 +205,9 @@ pub trait Assignment<F: Field> {
     fn copy(
         &mut self,
         permutation: &Permutation,
-        left_column: usize,
+        left_column: Column<Any>,
         left_row: usize,
-        right_column: usize,
+        right_column: Column<Any>,
         right_row: usize,
     ) -> Result<(), Error>;
 
diff --git a/src/plonk/keygen.rs b/src/plonk/keygen.rs
index 7531ec6..dfe0fe2 100644
--- a/src/plonk/keygen.rs
+++ b/src/plonk/keygen.rs
@@ -2,7 +2,7 @@ use ff::Field;
 use group::Curve;
 
 use super::{
-    circuit::{Advice, Assignment, Circuit, Column, ConstraintSystem, Fixed},
+    circuit::{Advice, Any, Assignment, Circuit, Column, ConstraintSystem, Fixed},
     permutation, Error, LagrangeCoeff, Permutation, Polynomial, ProvingKey, VerifyingKey,
 };
 use crate::arithmetic::CurveAffine;
@@ -117,9 +117,9 @@ impl<F: Field> Assignment<F> for Assembly<F> {
     fn copy(
         &mut self,
         permutation: &Permutation,
-        left_column: usize,
+        left_column: Column<Any>,
         left_row: usize,
-        right_column: usize,
+        right_column: Column<Any>,
         right_row: usize,
     ) -> Result<(), Error> {
         // Check bounds first
@@ -127,7 +127,23 @@ impl<F: Field> Assignment<F> for Assembly<F> {
             return Err(Error::BoundsFailure);
         }
 
-        self.permutations[permutation.index()].copy(left_column, left_row, right_column, right_row)
+        let left_column_index = permutation
+            .mapping()
+            .iter()
+            .position(|c| c == &left_column)
+            .ok_or(Error::SynthesisError)?;
+        let right_column_index = permutation
+            .mapping()
+            .iter()
+            .position(|c| c == &right_column)
+            .ok_or(Error::SynthesisError)?;
+
+        self.permutations[permutation.index()].copy(
+            left_column_index,
+            left_row,
+            right_column_index,
+            right_row,
+        )
     }
 
     fn push_namespace<NR, N>(&mut self, _: N)
diff --git a/src/plonk/prover.rs b/src/plonk/prover.rs
index 21b7680..1f3d986 100644
--- a/src/plonk/prover.rs
+++ b/src/plonk/prover.rs
@@ -3,7 +3,7 @@ use group::Curve;
 use std::iter;
 
 use super::{
-    circuit::{Advice, Assignment, Circuit, Column, ConstraintSystem, Fixed},
+    circuit::{Advice, Any, Assignment, Circuit, Column, ConstraintSystem, Fixed},
     lookup, permutation, vanishing, ChallengeBeta, ChallengeGamma, ChallengeTheta, ChallengeX,
     ChallengeY, Error, Permutation, ProvingKey,
 };
@@ -160,9 +160,9 @@ pub fn create_proof<C: CurveAffine, T: TranscriptWrite<C>, ConcreteCircuit: Circ
                 fn copy(
                     &mut self,
                     _: &Permutation,
+                    _: Column<Any>,
                     _: usize,
-                    _: usize,
-                    _: usize,
+                    _: Column<Any>,
                     _: usize,
                 ) -> Result<(), Error> {
                     // We only care about advice columns here