diff --git a/src/human_encoding/named_node.rs b/src/human_encoding/named_node.rs
index a4d208a6..f282d6f0 100644
--- a/src/human_encoding/named_node.rs
+++ b/src/human_encoding/named_node.rs
@@ -413,17 +413,13 @@ impl<J: Jet> NamedConstructNode<J> {
                 if self.for_main {
                     // For `main`, only apply type ascriptions *after* inference has completely
                     // determined the type.
-                    let source_bound =
-                        types::Bound::Complete(Arc::clone(&commit_data.arrow().source));
-                    let source_ty = types::Type::from(source_bound);
+                    let source_ty = types::Type::complete(Arc::clone(&commit_data.arrow().source));
                     for ty in data.node.cached_data().user_source_types.as_ref() {
                         if let Err(e) = source_ty.unify(ty, "binding source type annotation") {
                             self.errors.add(data.node.position(), e);
                         }
                     }
-                    let target_bound =
-                        types::Bound::Complete(Arc::clone(&commit_data.arrow().target));
-                    let target_ty = types::Type::from(target_bound);
+                    let target_ty = types::Type::complete(Arc::clone(&commit_data.arrow().target));
                     for ty in data.node.cached_data().user_target_types.as_ref() {
                         if let Err(e) = target_ty.unify(ty, "binding target type annotation") {
                             self.errors.add(data.node.position(), e);
diff --git a/src/human_encoding/parse/ast.rs b/src/human_encoding/parse/ast.rs
index 241b606b..f58e9d4e 100644
--- a/src/human_encoding/parse/ast.rs
+++ b/src/human_encoding/parse/ast.rs
@@ -633,9 +633,7 @@ fn grammar<J: Jet + 'static>() -> Grammar<Ast<J>> {
                     Error::BadWordLength { bit_length },
                 ));
             }
-            let ty = types::Type::two_two_n(bit_length.trailing_zeros() as usize)
-                .final_data()
-                .unwrap();
+            let ty = types::Final::two_two_n(bit_length.trailing_zeros() as usize);
             // unwrap ok here since literally every sequence of bits is a valid
             // value for the given type
             let value = iter.read_value(&ty).unwrap();
diff --git a/src/types/final_data.rs b/src/types/final_data.rs
index 1bfc06e9..8858edd3 100644
--- a/src/types/final_data.rs
+++ b/src/types/final_data.rs
@@ -12,7 +12,6 @@
 //!
 
 use crate::dag::{Dag, DagLike, NoSharing};
-use crate::types::{Bound, Type};
 use crate::Tmr;
 
 use std::sync::Arc;
@@ -163,7 +162,7 @@ impl Final {
     ///
     /// The type is precomputed and fast to access.
     pub fn two_two_n(n: usize) -> Arc<Self> {
-        super::precomputed::nth_power_of_2(n).final_data().unwrap()
+        super::precomputed::nth_power_of_2(n)
     }
 
     /// Create the sum of the given `left` and `right` types.
@@ -227,12 +226,6 @@ impl Final {
     }
 }
 
-impl From<Arc<Final>> for Type {
-    fn from(value: Arc<Final>) -> Self {
-        Type::from(Bound::Complete(value))
-    }
-}
-
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/src/types/mod.rs b/src/types/mod.rs
index 3aad8f91..9461008e 100644
--- a/src/types/mod.rs
+++ b/src/types/mod.rs
@@ -402,7 +402,7 @@ impl Type {
     ///
     /// The type is precomputed and fast to access.
     pub fn two_two_n(n: usize) -> Self {
-        precomputed::nth_power_of_2(n)
+        Self::complete(precomputed::nth_power_of_2(n))
     }
 
     /// Create the sum of the given `left` and `right` types.
@@ -415,6 +415,11 @@ impl Type {
         Type::from(Bound::product(left, right))
     }
 
+    /// Create a complete type.
+    pub fn complete(final_data: Arc<Final>) -> Self {
+        Type::from(Bound::Complete(final_data))
+    }
+
     /// Clones the `Type`.
     ///
     /// This is the same as just calling `.clone()` but has a different name to
diff --git a/src/types/precomputed.rs b/src/types/precomputed.rs
index 86d6a683..fb67ae32 100644
--- a/src/types/precomputed.rs
+++ b/src/types/precomputed.rs
@@ -14,33 +14,34 @@
 
 use crate::Tmr;
 
-use super::Type;
+use super::Final;
 
 use std::cell::RefCell;
 use std::convert::TryInto;
+use std::sync::Arc;
 
 // Directly use the size of the precomputed TMR table to make sure they're in sync.
 const N_POWERS: usize = Tmr::POWERS_OF_TWO.len();
 
 thread_local! {
-    static POWERS_OF_TWO: RefCell<Option<[Type; N_POWERS]>> = RefCell::new(None);
+    static POWERS_OF_TWO: RefCell<Option<[Arc<Final>; N_POWERS]>> = RefCell::new(None);
 }
 
-fn initialize(write: &mut Option<[Type; N_POWERS]>) {
-    let one = Type::unit();
+fn initialize(write: &mut Option<[Arc<Final>; N_POWERS]>) {
+    let one = Final::unit();
     let mut powers = Vec::with_capacity(N_POWERS);
 
     // Two^(2^0) = Two = (One + One)
-    let mut power = Type::sum(one.shallow_clone(), one);
-    powers.push(power.shallow_clone());
+    let mut power = Final::sum(Arc::clone(&one), one);
+    powers.push(Arc::clone(&power));
 
     // Two^(2^(i + 1)) = (Two^(2^i) * Two^(2^i))
     for _ in 1..N_POWERS {
-        power = Type::product(power.shallow_clone(), power);
-        powers.push(power.shallow_clone());
+        power = Final::product(Arc::clone(&power), power);
+        powers.push(Arc::clone(&power));
     }
 
-    let powers: [Type; N_POWERS] = powers.try_into().unwrap();
+    let powers: [Arc<Final>; N_POWERS] = powers.try_into().unwrap();
     *write = Some(powers);
 }
 
@@ -49,12 +50,12 @@ fn initialize(write: &mut Option<[Type; N_POWERS]>) {
 /// # Panics
 ///
 /// Panics if you request a number `n` greater than or equal to [`Tmr::POWERS_OF_TWO`].
-pub fn nth_power_of_2(n: usize) -> Type {
+pub fn nth_power_of_2(n: usize) -> Arc<Final> {
     POWERS_OF_TWO.with(|arr| {
         if arr.borrow().is_none() {
             initialize(&mut arr.borrow_mut());
         }
         debug_assert!(arr.borrow().is_some());
-        arr.borrow().as_ref().unwrap()[n].shallow_clone()
+        Arc::clone(&arr.borrow().as_ref().unwrap()[n])
     })
 }