diff --git a/benches/plonk.rs b/benches/plonk.rs
index bf48509..1204336 100644
--- a/benches/plonk.rs
+++ b/benches/plonk.rs
@@ -20,7 +20,7 @@ fn bench_with_k(name: &str, k: u32, c: &mut Criterion) {
     // Initialize the polynomial commitment parameters
     let params: Params<EqAffine> = Params::new(k);
 
-    #[derive(Copy, Clone)]
+    #[derive(Clone)]
     struct PLONKConfig {
         a: Column<Advice>,
         b: Column<Advice>,
@@ -31,7 +31,7 @@ fn bench_with_k(name: &str, k: u32, c: &mut Criterion) {
         sc: Column<Fixed>,
         sm: Column<Fixed>,
 
-        perm: usize,
+        perm: Permutation,
     }
 
     trait StandardCS<FF: FieldExt> {
@@ -156,21 +156,13 @@ fn bench_with_k(name: &str, k: u32, c: &mut Criterion) {
             ))
         }
         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.1, right_column, right.1)
+            self.cs.copy(
+                &self.config.perm,
+                left.0.into(),
+                left.1,
+                right.0.into(),
+                right.1,
+            )
         }
     }
 
diff --git a/examples/circuit-layout.rs b/examples/circuit-layout.rs
index ccd9338..14417e8 100644
--- a/examples/circuit-layout.rs
+++ b/examples/circuit-layout.rs
@@ -2,7 +2,7 @@ use halo2::{
     arithmetic::FieldExt,
     dev::circuit_layout,
     pasta::Fp,
-    plonk::{Advice, Assignment, Circuit, Column, ConstraintSystem, Error, Fixed},
+    plonk::{Advice, Assignment, Circuit, Column, ConstraintSystem, Error, Fixed, Permutation},
     poly::Rotation,
 };
 use plotters::prelude::*;
@@ -30,8 +30,8 @@ fn main() {
         sl: Column<Fixed>,
         sl2: Column<Fixed>,
 
-        perm: usize,
-        perm2: usize,
+        perm: Permutation,
+        perm2: Permutation,
     }
 
     trait StandardCS<FF: FieldExt> {
@@ -195,26 +195,18 @@ fn main() {
             ))
         }
         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.1, right_column, right.1)?;
             self.cs.copy(
-                self.config.perm2,
-                left_column,
+                &self.config.perm,
+                left.0.into(),
                 left.1,
-                right_column,
+                right.0.into(),
+                right.1,
+            )?;
+            self.cs.copy(
+                &self.config.perm2,
+                left.0.into(),
+                left.1,
+                right.0.into(),
                 right.1,
             )
         }
diff --git a/src/dev/graph.rs b/src/dev/graph.rs
index 6484864..cce172f 100644
--- a/src/dev/graph.rs
+++ b/src/dev/graph.rs
@@ -1,7 +1,9 @@
 use ff::Field;
 use tabbycat::{AttrList, Edge, GraphBuilder, GraphType, Identity, StmtList};
 
-use crate::plonk::{Advice, Assignment, Circuit, Column, ConstraintSystem, Error, Fixed};
+use crate::plonk::{
+    Advice, Any, Assignment, Circuit, Column, ConstraintSystem, Error, Fixed, Permutation,
+};
 
 pub mod layout;
 
@@ -118,10 +120,10 @@ impl<F: Field> Assignment<F> for Graph {
 
     fn copy(
         &mut self,
+        _: &Permutation,
+        _: Column<Any>,
         _: usize,
-        _: usize,
-        _: usize,
-        _: usize,
+        _: Column<Any>,
         _: usize,
     ) -> Result<(), crate::plonk::Error> {
         // Do nothing; we don't care about permutations in this context.
diff --git a/src/dev/graph/layout.rs b/src/dev/graph/layout.rs
index 71a91fc..5883253 100644
--- a/src/dev/graph/layout.rs
+++ b/src/dev/graph/layout.rs
@@ -6,7 +6,9 @@ use plotters::{
 use std::cmp;
 use std::collections::HashSet;
 
-use crate::plonk::{Advice, Any, Assignment, Circuit, Column, ConstraintSystem, Error, Fixed};
+use crate::plonk::{
+    Advice, Any, Assignment, Circuit, Column, ConstraintSystem, Error, Fixed, Permutation,
+};
 
 /// Renders the circuit layout on the given drawing area.
 ///
@@ -251,10 +253,10 @@ impl<F: Field> Assignment<F> for Layout {
 
     fn copy(
         &mut self,
+        _: &Permutation,
+        _: Column<Any>,
         _: usize,
-        _: usize,
-        _: usize,
-        _: usize,
+        _: Column<Any>,
         _: usize,
     ) -> Result<(), crate::plonk::Error> {
         // Do nothing; we don't care about permutations in this context.
diff --git a/src/plonk/circuit.rs b/src/plonk/circuit.rs
index 4893ddd..2f1bba6 100644
--- a/src/plonk/circuit.rs
+++ b/src/plonk/circuit.rs
@@ -201,7 +201,7 @@ pub trait Assignment<F: Field> {
         A: FnOnce() -> AR,
         AR: Into<String>;
 
-    /// Assign two advice columns to have the same value
+    /// Assign two cells to have the same value
     fn copy(
         &mut self,
         permutation: &Permutation,