diff --git a/crates/core/component/dex/src/batch_swap_output_data.rs b/crates/core/component/dex/src/batch_swap_output_data.rs
index f810136b38..2f384656a2 100644
--- a/crates/core/component/dex/src/batch_swap_output_data.rs
+++ b/crates/core/component/dex/src/batch_swap_output_data.rs
@@ -6,12 +6,12 @@ use ark_r1cs_std::{
     select::CondSelectGadget,
 };
 use ark_relations::r1cs::{ConstraintSystemRef, SynthesisError};
-use decaf377::{r1cs::FqVar, Fq};
+use decaf377::Fq;
 use penumbra_proto::{penumbra::core::component::dex::v1 as pb, DomainType};
-use penumbra_tct::Position;
+use penumbra_tct::{r1cs::PositionVar, Position};
 use serde::{Deserialize, Serialize};
 
-use penumbra_num::fixpoint::{bit_constrain, U128x128, U128x128Var};
+use penumbra_num::fixpoint::{U128x128, U128x128Var};
 use penumbra_num::{Amount, AmountVar};
 
 use crate::TradingPairVar;
@@ -130,19 +130,9 @@ impl ToConstraintField<Fq> for BatchSwapOutputData {
                 .expect("trading_pair is a Bls12-377 field member"),
         );
         public_inputs.extend(
-            Fq::from(self.epoch_starting_height)
+            self.sct_position_prefix
                 .to_field_elements()
-                .expect("Fq types are Bls12-377 field members"),
-        );
-        public_inputs.extend(
-            Fq::from(self.sct_position_prefix.epoch())
-                .to_field_elements()
-                .expect("Fq types are Bls12-377 field members"),
-        );
-        public_inputs.extend(
-            Fq::from(self.sct_position_prefix.block())
-                .to_field_elements()
-                .expect("Fq types are Bls12-377 field members"),
+                .expect("Position types are Bls12-377 field members"),
         );
         Some(public_inputs)
     }
@@ -156,8 +146,7 @@ pub struct BatchSwapOutputDataVar {
     pub unfilled_1: U128x128Var,
     pub unfilled_2: U128x128Var,
     pub trading_pair: TradingPairVar,
-    pub epoch: FqVar,
-    pub block: FqVar,
+    pub sct_position_prefix: PositionVar,
 }
 
 impl AllocVar<BatchSwapOutputData, Fq> for BatchSwapOutputDataVar {
@@ -181,28 +170,13 @@ impl AllocVar<BatchSwapOutputData, Fq> for BatchSwapOutputDataVar {
         let unfilled_1 = U128x128Var::new_variable(cs.clone(), || Ok(unfilled_1_fixpoint), mode)?;
         let unfilled_2_fixpoint: U128x128 = output_data.unfilled_2.into();
         let unfilled_2 = U128x128Var::new_variable(cs.clone(), || Ok(unfilled_2_fixpoint), mode)?;
-        let epoch = FqVar::new_variable(
-            cs.clone(),
-            || Ok(Fq::from(output_data.sct_position_prefix.epoch())),
-            mode,
-        )?;
-        let block = FqVar::new_variable(
-            cs.clone(),
-            || Ok(Fq::from(output_data.sct_position_prefix.block())),
-            mode,
-        )?;
-        // Check that epoch and block are 16 bits
-        let _ = bit_constrain(epoch.clone(), 16);
-        let _ = bit_constrain(block.clone(), 16);
         let trading_pair = TradingPairVar::new_variable_unchecked(
             cs.clone(),
             || Ok(output_data.trading_pair),
             mode,
         )?;
-        let epoch_starting_height =
-            FqVar::new_variable(cs, || Ok(Fq::from(output_data.epoch_starting_height)), mode)?;
-        // Check the epoch starting height is 64 bits
-        let _ = bit_constrain(epoch_starting_height.clone(), 64);
+        let sct_position_prefix =
+            PositionVar::new_variable(cs.clone(), || Ok(output_data.sct_position_prefix), mode)?;
 
         Ok(Self {
             delta_1,
@@ -212,8 +186,7 @@ impl AllocVar<BatchSwapOutputData, Fq> for BatchSwapOutputDataVar {
             unfilled_1,
             unfilled_2,
             trading_pair,
-            epoch,
-            block,
+            sct_position_prefix,
         })
     }
 }
@@ -454,10 +427,10 @@ mod tests {
                     lambda_2: Amount::from(1u32),
                     unfilled_1: Amount::from(1u32),
                     unfilled_2: Amount::from(1u32),
-                    height: 1,
+                    height: 0,
                     trading_pair,
-                    epoch_starting_height: 1,
-                    sct_position_prefix: Position::default(),
+                    epoch_starting_height: 0,
+                    sct_position_prefix: 0u64.into(),
                 },
             }
         }
diff --git a/crates/core/component/dex/src/swap_claim/proof.rs b/crates/core/component/dex/src/swap_claim/proof.rs
index e90a863277..7484e1d307 100644
--- a/crates/core/component/dex/src/swap_claim/proof.rs
+++ b/crates/core/component/dex/src/swap_claim/proof.rs
@@ -261,10 +261,12 @@ impl ConstraintSynthesizer<Fq> for SwapClaimCircuit {
 
         // Validate the swap commitment's height matches the output data's height (i.e. the clearing price height).
         output_data_var
-            .block
+            .sct_position_prefix
+            .block()?
             .enforce_equal(&position_var.block()?)?;
         output_data_var
-            .epoch
+            .sct_position_prefix
+            .epoch()?
             .enforce_equal(&position_var.epoch()?)?;
 
         // Validate that the output data's trading pair matches the note commitment's trading pair.