diff --git a/src/circuit/gadget/ecc/chip.rs b/src/circuit/gadget/ecc/chip.rs
index 0ce5f6bd..ab02c99a 100644
--- a/src/circuit/gadget/ecc/chip.rs
+++ b/src/circuit/gadget/ecc/chip.rs
@@ -149,7 +149,7 @@ pub struct EccConfig {
     /// Variable-base scalar multiplication (lo half)
     mul_lo: mul::incomplete::Config<{ mul::INCOMPLETE_LO_LEN }>,
     /// Selector used to enforce boolean decomposition in variable-base scalar mul
-    pub q_mul_decompose_var: Selector,
+    pub mul_complete: mul::complete::Config,
     /// Selector used to enforce switching logic on LSB in variable-base scalar mul
     pub q_mul_lsb: Selector,
     /// Variable-base scalar multiplication (overflow check)
@@ -228,9 +228,6 @@ impl EccChip {
         // - advices[4]: lambda1
         // - advices[9]: z
         //
-        // mul::complete::Config:
-        // - advices[9]: z_complete
-        //
         // TODO: Refactor away from `impl From<EccConfig> for _` so that sub-configs can
         // equality-enable the columns they need to.
         for column in &advices {
@@ -261,6 +258,7 @@ impl EccChip {
         let mul_lo = mul::incomplete::Config::configure(
             meta, advices[6], advices[7], advices[0], advices[1], advices[8], advices[2],
         );
+        let mul_complete = mul::complete::Config::configure(meta, advices[9], add);
 
         let config = EccConfig {
             advices,
@@ -270,7 +268,7 @@ impl EccChip {
             add,
             mul_hi,
             mul_lo,
-            q_mul_decompose_var: meta.selector(),
+            mul_complete,
             q_mul_overflow: meta.selector(),
             q_mul_lsb: meta.selector(),
             q_mul_fixed_full: meta.selector(),
diff --git a/src/circuit/gadget/ecc/chip/mul.rs b/src/circuit/gadget/ecc/chip/mul.rs
index a95e0831..21dad7b1 100644
--- a/src/circuit/gadget/ecc/chip/mul.rs
+++ b/src/circuit/gadget/ecc/chip/mul.rs
@@ -16,7 +16,8 @@ use halo2::{
 
 use pasta_curves::pallas;
 
-mod complete;
+// TODO: Undo this pub(crate).
+pub(crate) mod complete;
 // TODO: Undo this pub(crate).
 pub(crate) mod incomplete;
 mod overflow;
@@ -67,7 +68,7 @@ impl From<&EccConfig> for Config {
             add_config: ecc_config.add,
             hi_config: ecc_config.mul_hi,
             lo_config: ecc_config.mul_lo,
-            complete_config: ecc_config.into(),
+            complete_config: ecc_config.mul_complete,
             overflow_config: ecc_config.into(),
         };
 
@@ -111,7 +112,6 @@ impl From<&EccConfig> for Config {
 
 impl Config {
     pub(super) fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
-        self.complete_config.create_gate(meta);
         self.overflow_config.create_gate(meta);
 
         // If `lsb` is 0, (x, y) = (x_p, -y_p). If `lsb` is 1, (x, y) = (0,0).
diff --git a/src/circuit/gadget/ecc/chip/mul/complete.rs b/src/circuit/gadget/ecc/chip/mul/complete.rs
index 585261a2..5c5ce049 100644
--- a/src/circuit/gadget/ecc/chip/mul/complete.rs
+++ b/src/circuit/gadget/ecc/chip/mul/complete.rs
@@ -1,4 +1,4 @@
-use super::super::{add, copy, CellValue, EccConfig, EccPoint, Var};
+use super::super::{add, copy, CellValue, EccPoint, Var};
 use super::{COMPLETE_RANGE, X, Y, Z};
 use crate::circuit::gadget::utilities::{bool_check, ternary};
 
@@ -10,6 +10,7 @@ use halo2::{
 
 use pasta_curves::{arithmetic::FieldExt, pallas};
 
+#[derive(Copy, Clone, Debug, Eq, PartialEq)]
 pub struct Config {
     // Selector used to constrain the cells used in complete addition.
     q_mul_decompose_var: Selector,
@@ -19,30 +20,31 @@ pub struct Config {
     add_config: add::Config,
 }
 
-impl From<&EccConfig> for Config {
-    fn from(ecc_config: &EccConfig) -> Self {
+impl Config {
+    /// TODO: Make this pub(super).
+    pub(crate) fn configure(
+        meta: &mut ConstraintSystem<pallas::Base>,
+        z_complete: Column<Advice>,
+        add_config: add::Config,
+    ) -> Self {
+        meta.enable_equality(z_complete.into());
+
         let config = Self {
-            q_mul_decompose_var: ecc_config.q_mul_decompose_var,
-            z_complete: ecc_config.advices[9],
-            add_config: ecc_config.add,
+            q_mul_decompose_var: meta.selector(),
+            z_complete,
+            add_config,
         };
 
-        let add_config_advices = config.add_config.advice_columns();
-        assert!(
-            !add_config_advices.contains(&config.z_complete),
-            "z_complete cannot overlap with complete addition columns."
-        );
+        config.create_gate(meta);
 
         config
     }
-}
 
-impl Config {
     /// Gate used to check scalar decomposition is correct.
     /// This is used to check the bits used in complete addition, since the incomplete
     /// addition gate (controlled by `q_mul`) already checks scalar decomposition for
     /// the other bits.
-    pub(super) fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
+    fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
         // | y_p | z_complete |
         // --------------------
         // | y_p | z_{i + 1}  |