diff --git a/src/builder.rs b/src/builder.rs
index 6ed10616..0165332e 100644
--- a/src/builder.rs
+++ b/src/builder.rs
@@ -154,7 +154,7 @@ impl ActionInfo {
                 cv_net,
                 SigningMetadata {
                     dummy_ask: self.spend.dummy_sk.as_ref().map(SpendAuthorizingKey::from),
-                    ak,
+                    parts: SigningParts { ak, alpha },
                 },
             ),
             Circuit {},
@@ -325,6 +325,16 @@ impl Builder {
     }
 }
 
+/// The parts needed to sign an [`Action`].
+#[derive(Debug)]
+pub struct SigningParts {
+    /// The spend validating key for this action. Used to match spend authorizing keys to
+    /// actions they can create signatures for.
+    ak: SpendValidatingKey,
+    /// The randomization needed to derive the actual signing key for this note.
+    alpha: pallas::Scalar,
+}
+
 /// Marker for an unauthorized bundle, with a proof but no signatures.
 #[derive(Debug)]
 pub struct Unauthorized {
@@ -345,9 +355,7 @@ pub struct SigningMetadata {
     /// These keys are used automatically in [`Bundle<Unauthorized>::prepare`] or
     /// [`Bundle<Unauthorized>::apply_signatures`] to sign dummy spends.
     dummy_ask: Option<SpendAuthorizingKey>,
-    /// The spend validating key for this action. Used to match spend authorizing keys to
-    /// actions they can create signatures for.
-    ak: SpendValidatingKey,
+    parts: SigningParts,
 }
 
 /// Marker for a partially-authorized bundle, in the process of being signed.
@@ -359,7 +367,27 @@ pub struct PartiallyAuthorized {
 }
 
 impl Authorization for PartiallyAuthorized {
-    type SpendAuth = (Option<redpallas::Signature<SpendAuth>>, SpendValidatingKey);
+    type SpendAuth = MaybeSigned;
+}
+
+/// A heisen[`Signature`] for a particular [`Action`].
+///
+/// [`Signature`]: redpallas::Signature
+#[derive(Debug)]
+pub enum MaybeSigned {
+    /// The information needed to sign this [`Action`].
+    SigningMetadata(SigningParts),
+    /// The signature for this [`Action`].
+    Signature(redpallas::Signature<SpendAuth>),
+}
+
+impl MaybeSigned {
+    fn finalize(self) -> Result<redpallas::Signature<SpendAuth>, Error> {
+        match self {
+            Self::Signature(sig) => Ok(sig),
+            _ => Err(Error::MissingSignatures),
+        }
+    }
 }
 
 impl<V> Bundle<Unauthorized, V> {
@@ -373,12 +401,12 @@ impl<V> Bundle<Unauthorized, V> {
     ) -> Bundle<PartiallyAuthorized, V> {
         self.authorize(
             &mut rng,
-            |rng, _, SigningMetadata { dummy_ask, ak }| {
-                (
-                    // We can create signatures for dummy spends immediately.
-                    dummy_ask.map(|ask| ask.sign(rng, &sighash)),
-                    ak,
-                )
+            |rng, _, SigningMetadata { dummy_ask, parts }| {
+                // We can create signatures for dummy spends immediately.
+                dummy_ask
+                    .map(|ask| ask.randomize(&parts.alpha).sign(rng, &sighash))
+                    .map(MaybeSigned::Signature)
+                    .unwrap_or(MaybeSigned::SigningMetadata(parts))
             },
             |rng, unauth| PartiallyAuthorized {
                 proof: unauth.proof,
@@ -412,17 +440,11 @@ impl<V> Bundle<PartiallyAuthorized, V> {
         let expected_ak = ask.into();
         self.authorize(
             &mut rng,
-            |rng, partial, (sig, ak)| {
-                (
-                    sig.or_else(|| {
-                        if ak == expected_ak {
-                            Some(ask.sign(rng, &partial.sighash))
-                        } else {
-                            None
-                        }
-                    }),
-                    ak,
-                )
+            |rng, partial, maybe| match maybe {
+                MaybeSigned::SigningMetadata(parts) if parts.ak == expected_ak => {
+                    MaybeSigned::Signature(ask.randomize(&parts.alpha).sign(rng, &partial.sighash))
+                }
+                s => s,
             },
             |_, partial| partial,
         )
@@ -434,10 +456,7 @@ impl<V> Bundle<PartiallyAuthorized, V> {
     pub fn finalize(self) -> Result<Bundle<Authorized, V>, Error> {
         self.try_authorize(
             &mut (),
-            |_, _, (sig, _)| match sig {
-                Some(sig) => Ok(sig),
-                None => Err(Error::MissingSignatures),
-            },
+            |_, _, maybe| maybe.finalize(),
             |_, partial| {
                 Ok(Authorized::from_parts(
                     partial.proof,
@@ -594,12 +613,12 @@ mod tests {
         builder
             .add_recipient(None, recipient, NoteValue::from_raw(5000), None)
             .unwrap();
-        let bundle: Bundle<Authorized, i64> = dbg!(builder
+        let bundle: Bundle<Authorized, i64> = builder
             .build(&mut rng, &pk)
             .unwrap()
-            .prepare(&mut rng, [0; 32]))
-        .finalize()
-        .unwrap();
+            .prepare(&mut rng, [0; 32])
+            .finalize()
+            .unwrap();
         assert_eq!(bundle.value_balance(), &(-5000))
     }
 }
diff --git a/src/keys.rs b/src/keys.rs
index 03f56bc9..63890442 100644
--- a/src/keys.rs
+++ b/src/keys.rs
@@ -8,7 +8,7 @@ use fpe::ff1::{BinaryNumeralString, FF1};
 use group::GroupEncoding;
 use halo2::arithmetic::FieldExt;
 use pasta_curves::pallas;
-use rand::{CryptoRng, RngCore};
+use rand::RngCore;
 use subtle::CtOption;
 
 use crate::{
@@ -76,13 +76,11 @@ impl SpendAuthorizingKey {
         to_scalar(PrfExpand::OrchardAsk.expand(&sk.0))
     }
 
-    /// Creates a spend authorization signature over the given message.
-    pub fn sign<R: RngCore + CryptoRng>(
-        &self,
-        rng: R,
-        msg: &[u8],
-    ) -> redpallas::Signature<SpendAuth> {
-        self.0.sign(rng, msg)
+    /// Randomizes this spend authorizing key with the given `randomizer`.
+    ///
+    /// The resulting key can be used to actually sign a spend.
+    pub fn randomize(&self, randomizer: &pallas::Scalar) -> redpallas::SigningKey<SpendAuth> {
+        self.0.randomize(randomizer)
     }
 }
 
diff --git a/src/primitives/redpallas.rs b/src/primitives/redpallas.rs
index e03529aa..db4d88c8 100644
--- a/src/primitives/redpallas.rs
+++ b/src/primitives/redpallas.rs
@@ -40,6 +40,15 @@ impl<T: SigType> TryFrom<[u8; 32]> for SigningKey<T> {
     }
 }
 
+impl SigningKey<SpendAuth> {
+    /// Randomizes this signing key with the given `randomizer`.
+    ///
+    /// Randomization is only supported for `SpendAuth` keys.
+    pub fn randomize(&self, randomizer: &pallas::Scalar) -> Self {
+        SigningKey(self.0.randomize(randomizer))
+    }
+}
+
 impl<T: SigType> SigningKey<T> {
     /// Creates a signature of type `T` on `msg` using this `SigningKey`.
     pub fn sign<R: RngCore + CryptoRng>(&self, rng: R, msg: &[u8]) -> Signature<T> {