diff --git a/src/jwk.rs b/src/jwk.rs
index 828f7b7..994205b 100644
--- a/src/jwk.rs
+++ b/src/jwk.rs
@@ -838,5 +838,5 @@ pub trait IntoJsonWebKey: Sealed {
     /// # Errors
     ///
     /// Returns an [`Err`] if the conversion fails.
-    fn into_jwk(self, alg: impl Into<Option<Self::Algorithm>>) -> Result<JsonWebKey, Self::Error>;
+    fn into_jwk(self, alg: Option<impl Into<Self::Algorithm>>) -> Result<JsonWebKey, Self::Error>;
 }
diff --git a/src/jwk/okp/curve25519/ed25519.rs b/src/jwk/okp/curve25519/ed25519.rs
index a43d4dd..9b647cb 100644
--- a/src/jwk/okp/curve25519/ed25519.rs
+++ b/src/jwk/okp/curve25519/ed25519.rs
@@ -135,14 +135,12 @@ impl IntoJsonWebKey for Ed25519PrivateKey {
     type Algorithm = ();
     type Error = Infallible;
 
-    fn into_jwk(self, alg: impl Into<Option<Self::Algorithm>>) -> Result<JsonWebKey, Self::Error> {
+    fn into_jwk(self, alg: Option<impl Into<Self::Algorithm>>) -> Result<JsonWebKey, Self::Error> {
         let key = JsonWebKeyType::Asymmetric(Box::new(AsymmetricJsonWebKey::Private(
             Private::Okp(OkpPrivate::Curve25519(Curve25519Private::Ed(self))),
         )));
         let mut jwk = JsonWebKey::new(key);
-        jwk.algorithm = alg
-            .into()
-            .map(|_| JsonWebAlgorithm::Signing(JsonWebSigningAlgorithm::EdDSA));
+        jwk.algorithm = alg.map(|_| JsonWebAlgorithm::Signing(JsonWebSigningAlgorithm::EdDSA));
         Ok(jwk)
     }
 }
@@ -152,14 +150,12 @@ impl IntoJsonWebKey for Ed25519PublicKey {
     type Algorithm = ();
     type Error = Infallible;
 
-    fn into_jwk(self, alg: impl Into<Option<Self::Algorithm>>) -> Result<JsonWebKey, Self::Error> {
+    fn into_jwk(self, alg: Option<impl Into<Self::Algorithm>>) -> Result<JsonWebKey, Self::Error> {
         let key = JsonWebKeyType::Asymmetric(Box::new(AsymmetricJsonWebKey::Public(Public::Okp(
             OkpPublic::Curve25519(Curve25519Public::Ed(self)),
         ))));
         let mut jwk = JsonWebKey::new(key);
-        jwk.algorithm = alg
-            .into()
-            .map(|_| JsonWebAlgorithm::Signing(JsonWebSigningAlgorithm::EdDSA));
+        jwk.algorithm = alg.map(|_| JsonWebAlgorithm::Signing(JsonWebSigningAlgorithm::EdDSA));
         Ok(jwk)
     }
 }
diff --git a/src/jwk/rsa.rs b/src/jwk/rsa.rs
index 722c0e7..c0c3958 100644
--- a/src/jwk/rsa.rs
+++ b/src/jwk/rsa.rs
@@ -39,11 +39,11 @@ impl IntoJsonWebKey for RsaPublicKey {
 
     fn into_jwk(
         self,
-        alg: impl Into<Option<Self::Algorithm>>,
+        alg: Option<impl Into<Self::Algorithm>>,
     ) -> Result<crate::JsonWebKey, Self::Error> {
-        let alg = alg
-            .into()
-            .map(|rsa| jwa::JsonWebAlgorithm::Signing(jwa::JsonWebSigningAlgorithm::Rsa(rsa)));
+        let alg = alg.map(|rsa| {
+            jwa::JsonWebAlgorithm::Signing(jwa::JsonWebSigningAlgorithm::Rsa(rsa.into()))
+        });
 
         let key = super::JsonWebKeyType::Asymmetric(Box::new(super::AsymmetricJsonWebKey::Public(
             super::Public::Rsa(self),
@@ -150,11 +150,11 @@ impl IntoJsonWebKey for RsaPrivateKey {
 
     fn into_jwk(
         self,
-        alg: impl Into<Option<Self::Algorithm>>,
+        alg: Option<impl Into<Self::Algorithm>>,
     ) -> Result<crate::JsonWebKey, Self::Error> {
-        let alg = alg
-            .into()
-            .map(|rsa| jwa::JsonWebAlgorithm::Signing(jwa::JsonWebSigningAlgorithm::Rsa(rsa)));
+        let alg = alg.map(|rsa| {
+            jwa::JsonWebAlgorithm::Signing(jwa::JsonWebSigningAlgorithm::Rsa(rsa.into()))
+        });
 
         let key = super::JsonWebKeyType::Asymmetric(Box::new(
             super::AsymmetricJsonWebKey::Private(super::Private::Rsa(Box::new(self))),
diff --git a/src/jwk/symmetric/hmac.rs b/src/jwk/symmetric/hmac.rs
index 66513fb..eaa4b3d 100644
--- a/src/jwk/symmetric/hmac.rs
+++ b/src/jwk/symmetric/hmac.rs
@@ -125,14 +125,14 @@ impl<H: HmacVariant> IntoJsonWebKey for HmacKey<H> {
 
     fn into_jwk(
         self,
-        alg: impl Into<Option<Self::Algorithm>>,
+        alg: Option<impl Into<Self::Algorithm>>,
     ) -> Result<crate::JsonWebKey, Self::Error> {
         let key = jwk::JsonWebKeyType::Symmetric(jwk::SymmetricJsonWebKey::OctetSequence(
             OctetSequence::new(self.key),
         ));
 
         let mut jwk = crate::JsonWebKey::new(key);
-        jwk.algorithm = alg.into().map(|_| JsonWebAlgorithm::Signing(H::ALGORITHM));
+        jwk.algorithm = alg.map(|_| JsonWebAlgorithm::Signing(H::ALGORITHM));
         Ok(jwk)
     }
 }
diff --git a/src/macros.rs b/src/macros.rs
index 8ff016a..39017b9 100644
--- a/src/macros.rs
+++ b/src/macros.rs
@@ -44,7 +44,7 @@ macro_rules! impl_ec {
 
             fn into_jwk(
                 self,
-                alg: impl Into<Option<Self::Algorithm>>,
+                alg: Option<impl Into<Self::Algorithm>>,
             ) -> Result<crate::JsonWebKey, Self::Error> {
                 let key = crate::jwk::JsonWebKeyType::Asymmetric(alloc::boxed::Box::new(
                     crate::jwk::AsymmetricJsonWebKey::Public(crate::jwk::Public::Ec(
@@ -53,7 +53,7 @@ macro_rules! impl_ec {
                 ));
 
                 let mut jwk = crate::JsonWebKey::new(key);
-                jwk.algorithm = alg.into().map(|_| crate::jwa::JsonWebAlgorithm::Signing($alg));
+                jwk.algorithm = alg.map(|_| crate::jwa::JsonWebAlgorithm::Signing($alg.into()));
                 Ok(jwk)
             }
         }
@@ -74,7 +74,7 @@ macro_rules! impl_ec {
 
             fn into_jwk(
                 self,
-                alg: impl Into<Option<Self::Algorithm>>,
+                alg: Option<impl Into<Self::Algorithm>>,
             ) -> Result<crate::JsonWebKey, Self::Error> {
                 let key = crate::jwk::JsonWebKeyType::Asymmetric(alloc::boxed::Box::new(
                     crate::jwk::AsymmetricJsonWebKey::Private(crate::jwk::Private::Ec(
@@ -83,7 +83,7 @@ macro_rules! impl_ec {
                 ));
 
                 let mut jwk = crate::JsonWebKey::new(key);
-                jwk.algorithm = alg.into().map(|_| crate::jwa::JsonWebAlgorithm::Signing($alg));
+                jwk.algorithm = alg.map(|_| crate::jwa::JsonWebAlgorithm::Signing($alg.into()));
                 Ok(jwk)
             }
         }