diff --git a/src/circuit/gadget/ecc/chip.rs b/src/circuit/gadget/ecc/chip.rs
index 956330b4..a12b7030 100644
--- a/src/circuit/gadget/ecc/chip.rs
+++ b/src/circuit/gadget/ecc/chip.rs
@@ -139,7 +139,7 @@ pub struct EccConfig {
     pub fixed_z: Column<Fixed>,
 
     /// Incomplete addition
-    pub q_add_incomplete: Selector,
+    add_incomplete: add_incomplete::Config,
 
     /// Complete addition
     pub q_add: Selector,
@@ -249,12 +249,15 @@ impl EccChip {
 
         // Create witness point gate
         let witness_point = witness_point::Config::configure(meta, advices[0], advices[1]);
+        // Create incomplete point addition gate
+        let add_incomplete =
+            add_incomplete::Config::configure(meta, advices[0], advices[1], advices[2], advices[3]);
 
         let config = EccConfig {
             advices,
             lagrange_coeffs,
             fixed_z: meta.fixed_column(),
-            q_add_incomplete: meta.selector(),
+            add_incomplete,
             q_add: meta.selector(),
             q_mul_hi: (meta.selector(), meta.selector(), meta.selector()),
             q_mul_lo: (meta.selector(), meta.selector(), meta.selector()),
@@ -270,12 +273,6 @@ impl EccChip {
             running_sum_config,
         };
 
-        // Create incomplete point addition gate
-        {
-            let config: add_incomplete::Config = (&config).into();
-            config.create_gate(meta);
-        }
-
         // Create complete point addition gate
         {
             let add_config: add::Config = (&config).into();
@@ -432,7 +429,7 @@ impl EccInstructions<pallas::Affine> for EccChip {
         a: &Self::NonIdentityPoint,
         b: &Self::NonIdentityPoint,
     ) -> Result<Self::NonIdentityPoint, Error> {
-        let config: add_incomplete::Config = self.config().into();
+        let config = self.config().add_incomplete;
         layouter.assign_region(
             || "incomplete point addition",
             |mut region| config.assign_region(a, b, 0, &mut region),
diff --git a/src/circuit/gadget/ecc/chip/add_incomplete.rs b/src/circuit/gadget/ecc/chip/add_incomplete.rs
index a5da1875..30b74e0d 100644
--- a/src/circuit/gadget/ecc/chip/add_incomplete.rs
+++ b/src/circuit/gadget/ecc/chip/add_incomplete.rs
@@ -1,6 +1,6 @@
 use std::{array, collections::HashSet};
 
-use super::{copy, CellValue, EccConfig, NonIdentityEccPoint, Var};
+use super::{copy, CellValue, NonIdentityEccPoint, Var};
 use group::Curve;
 use halo2::{
     circuit::Region,
@@ -9,7 +9,7 @@ use halo2::{
 };
 use pasta_curves::{arithmetic::CurveAffine, pallas};
 
-#[derive(Clone, Debug)]
+#[derive(Clone, Copy, Debug, Eq, PartialEq)]
 pub struct Config {
     q_add_incomplete: Selector,
     // x-coordinate of P in P + Q = R
@@ -22,24 +22,37 @@ pub struct Config {
     pub y_qr: Column<Advice>,
 }
 
-impl From<&EccConfig> for Config {
-    fn from(ecc_config: &EccConfig) -> Self {
-        Self {
-            q_add_incomplete: ecc_config.q_add_incomplete,
-            x_p: ecc_config.advices[0],
-            y_p: ecc_config.advices[1],
-            x_qr: ecc_config.advices[2],
-            y_qr: ecc_config.advices[3],
-        }
-    }
-}
-
 impl Config {
+    pub(super) fn configure(
+        meta: &mut ConstraintSystem<pallas::Base>,
+        x_p: Column<Advice>,
+        y_p: Column<Advice>,
+        x_qr: Column<Advice>,
+        y_qr: Column<Advice>,
+    ) -> Self {
+        meta.enable_equality(x_p.into());
+        meta.enable_equality(y_p.into());
+        meta.enable_equality(x_qr.into());
+        meta.enable_equality(y_qr.into());
+
+        let config = Self {
+            q_add_incomplete: meta.selector(),
+            x_p,
+            y_p,
+            x_qr,
+            y_qr,
+        };
+
+        config.create_gate(meta);
+
+        config
+    }
+
     pub(crate) fn advice_columns(&self) -> HashSet<Column<Advice>> {
         core::array::IntoIter::new([self.x_p, self.y_p, self.x_qr, self.y_qr]).collect()
     }
 
-    pub(super) fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
+    fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
         meta.create_gate("incomplete addition gates", |meta| {
             let q_add_incomplete = meta.query_selector(self.q_add_incomplete);
             let x_p = meta.query_advice(self.x_p, Rotation::cur());
diff --git a/src/circuit/gadget/ecc/chip/mul_fixed.rs b/src/circuit/gadget/ecc/chip/mul_fixed.rs
index 87c2e376..bb2b87a8 100644
--- a/src/circuit/gadget/ecc/chip/mul_fixed.rs
+++ b/src/circuit/gadget/ecc/chip/mul_fixed.rs
@@ -108,7 +108,7 @@ impl<const NUM_WINDOWS: usize> From<&EccConfig> for Config<NUM_WINDOWS> {
             window: ecc_config.advices[4],
             u: ecc_config.advices[5],
             add_config: ecc_config.into(),
-            add_incomplete_config: ecc_config.into(),
+            add_incomplete_config: ecc_config.add_incomplete,
         };
 
         // Check relationships between this config and `add_config`.