diff --git a/src/backends/plonky2/basetypes.rs b/src/backends/plonky2/basetypes.rs
index d4c8f9b..813fbfa 100644
--- a/src/backends/plonky2/basetypes.rs
+++ b/src/backends/plonky2/basetypes.rs
@@ -2,17 +2,16 @@
 //! is enabled.
 //! See src/middleware/basetypes.rs for more details.
 
+/// F is the native field we use everywhere.  Currently it's Goldilocks from plonky2
+pub use plonky2::field::goldilocks_field::GoldilocksField as F;
 use plonky2::{
-    field::{extension::quadratic::QuadraticExtension, goldilocks_field::GoldilocksField},
+    field::extension::quadratic::QuadraticExtension,
     hash::{hash_types, poseidon::PoseidonHash},
     plonk::{circuit_builder, circuit_data, config::GenericConfig, proof},
 };
 use schemars::JsonSchema;
 use serde::{Deserialize, Deserializer, Serialize};
 
-/// F is the native field we use everywhere.  Currently it's Goldilocks from plonky2
-pub type F = GoldilocksField;
-
 /// D defines the extension degree of the field used in the Plonky2 proofs (quadratic extension).
 pub const D: usize = 2;
 
diff --git a/src/backends/plonky2/circuits/mainpod.rs b/src/backends/plonky2/circuits/mainpod.rs
index 2d1a7fa..326a3eb 100644
--- a/src/backends/plonky2/circuits/mainpod.rs
+++ b/src/backends/plonky2/circuits/mainpod.rs
@@ -41,7 +41,7 @@ use crate::{
     middleware::{
         AnchoredKey, CustomPredicate, CustomPredicateBatch, CustomPredicateRef, NativeOperation,
         NativePredicate, Params, PodType, PredicatePrefix, Statement, StatementArg, ToFields,
-        Value, ValueRef, EMPTY_VALUE, F, HASH_SIZE, KEY_TYPE, SELF, VALUE_SIZE,
+        Value, ValueRef, F, HASH_SIZE, KEY_TYPE, SELF, VALUE_SIZE,
     },
 };
 
@@ -947,7 +947,6 @@ fn normalize_statement_circuit(
     statement: &StatementTarget,
     self_id: &ValueTarget,
 ) -> StatementTarget {
-    let zero_value = builder.constant_value(EMPTY_VALUE);
     let self_value = builder.constant_value(SELF.0.into());
     let args = statement
         .args
@@ -955,11 +954,8 @@ fn normalize_statement_circuit(
         .map(|arg| {
             let first = ValueTarget::from_slice(&arg.elements[..VALUE_SIZE]);
             let second = ValueTarget::from_slice(&arg.elements[VALUE_SIZE..]);
-            let is_not_ak = builder.is_equal_flattenable(&zero_value, &second);
-            let is_ak = builder.not(is_not_ak);
             let is_self = builder.is_equal_flattenable(&self_value, &first);
-            let normalize = builder.and(is_ak, is_self);
-            let first_normalized = builder.select_flattenable(params, normalize, self_id, &first);
+            let first_normalized = builder.select_flattenable(params, is_self, self_id, &first);
             StatementArgTarget::new(first_normalized, second)
         })
         .collect_vec();
diff --git a/src/lang/mod.rs b/src/lang/mod.rs
index dd1c2f2..9248ced 100644
--- a/src/lang/mod.rs
+++ b/src/lang/mod.rs
@@ -31,7 +31,7 @@ mod tests {
         middleware::{
             hash_str, CustomPredicate, CustomPredicateBatch, CustomPredicateRef, Key,
             NativePredicate, Params, PodId, PodType, Predicate, RawValue, StatementTmpl,
-            StatementTmplArg, Value, Wildcard, KEY_SIGNER, KEY_TYPE, SELF_ID_HASH,
+            StatementTmplArg, Value, Wildcard, KEY_SIGNER, KEY_TYPE,
         },
     };
 
@@ -125,7 +125,7 @@ mod tests {
                 pred: Predicate::Native(NativePredicate::Equal),
                 args: vec![
                     sta_ak(("ConstPod", 0), "my_val"), // ?ConstPod["my_val"] -> Wildcard(0), Key("my_val")
-                    sta_lit(SELF_ID_HASH),
+                    sta_lit(RawValue::from(1)),
                 ],
             },
             StatementTmpl {
diff --git a/src/middleware/basetypes.rs b/src/middleware/basetypes.rs
index e187a30..97ed113 100644
--- a/src/middleware/basetypes.rs
+++ b/src/middleware/basetypes.rs
@@ -55,7 +55,7 @@ pub const HASH_SIZE: usize = 4;
 pub const VALUE_SIZE: usize = 4;
 
 pub const EMPTY_VALUE: RawValue = RawValue([F::ZERO, F::ZERO, F::ZERO, F::ZERO]);
-pub const SELF_ID_HASH: Hash = Hash([F::ONE, F::ZERO, F::ZERO, F::ZERO]);
+pub const SELF_ID_HASH: Hash = Hash([F(0x5), F(0xe), F(0x1), F(0xf)]);
 pub const EMPTY_HASH: Hash = Hash([F::ZERO, F::ZERO, F::ZERO, F::ZERO]);
 
 #[derive(Clone, Copy, Debug, Default, Hash, PartialEq, Eq, Serialize, Deserialize, JsonSchema)]
diff --git a/src/middleware/mod.rs b/src/middleware/mod.rs
index 51df8a7..2c7f53a 100644
--- a/src/middleware/mod.rs
+++ b/src/middleware/mod.rs
@@ -766,7 +766,7 @@ impl Params {
     }
 }
 
-/// Replace references to SELF by `self_id` in anchored keys of the statement.
+/// Replace references to SELF by `self_id`.
 pub fn normalize_statement(statement: &Statement, self_id: PodId) -> Statement {
     let predicate = statement.predicate();
     let args = statement
@@ -776,6 +776,9 @@ pub fn normalize_statement(statement: &Statement, self_id: PodId) -> Statement {
             StatementArg::Key(AnchoredKey { pod_id, key }) if *pod_id == SELF => {
                 StatementArg::Key(AnchoredKey::new(self_id, key.clone()))
             }
+            StatementArg::Literal(value) if value.raw.0 == SELF.0 .0 => {
+                StatementArg::Literal(self_id.into())
+            }
             _ => sa.clone(),
         })
         .collect();