diff --git a/Cargo.toml b/Cargo.toml
index 33a0328..737c4af 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -16,6 +16,7 @@ categories = [
 
 [dependencies]
 base64ct = { version = "1.6.0", features = ["std"] }
+bytes = { version = "1.5" }
 chrono = { version = "0.4.24", features = ["serde"] }
 elliptic-curve = { version = "0.13.4", features = [
     "pkcs8",
diff --git a/src/algorithms/ecdsa.rs b/src/algorithms/ecdsa.rs
index 7d76f3c..75a1235 100644
--- a/src/algorithms/ecdsa.rs
+++ b/src/algorithms/ecdsa.rs
@@ -74,7 +74,9 @@ use ::ecdsa::{
     PrimeCurve, SignatureSize,
 };
 use base64ct::Encoding;
+use bytes::BytesMut;
 use digest::generic_array::ArrayLength;
+use ecdsa::{hazmat::VerifyPrimitive, Signature, VerifyingKey};
 use elliptic_curve::{
     ops::Invert,
     sec1::{Coordinates, FromEncodedPoint, ModulusSize, ToEncodedPoint},
@@ -92,6 +94,7 @@ pub use p384::NistP384;
 
 #[cfg(feature = "p521")]
 pub use p521::NistP521;
+use signature::Verifier;
 
 impl<C> crate::key::JWKeyType for PublicKey<C>
 where
@@ -109,7 +112,7 @@ where
     FieldBytesSize<C>: ModulusSize,
 {
     fn parameters(&self) -> Vec<(String, serde_json::Value)> {
-        let mut params = Vec::with_capacity(2);
+        let mut params = Vec::with_capacity(3);
 
         params.push((
             "crv".to_owned(),
@@ -144,6 +147,31 @@ where
         self.public_key().parameters()
     }
 }
+
+impl<C> crate::key::SerializeJWK for ecdsa::VerifyingKey<C>
+where
+    C: PrimeCurve + CurveArithmetic + JwkParameters,
+    Scalar<C>: Invert<Output = CtOption<Scalar<C>>> + SignPrimitive<C>,
+    SignatureSize<C>: ArrayLength<u8>,
+    AffinePoint<C>: FromEncodedPoint<C> + ToEncodedPoint<C>,
+    FieldBytesSize<C>: ModulusSize,
+{
+    fn parameters(&self) -> Vec<(String, serde_json::Value)> {
+        PublicKey::<C>::from(self).parameters()
+    }
+}
+
+impl<C> crate::key::JWKeyType for ecdsa::VerifyingKey<C>
+where
+    C: PrimeCurve + CurveArithmetic + JwkParameters,
+    Scalar<C>: Invert<Output = CtOption<Scalar<C>>> + SignPrimitive<C>,
+    SignatureSize<C>: ArrayLength<u8>,
+    AffinePoint<C>: FromEncodedPoint<C> + ToEncodedPoint<C>,
+    FieldBytesSize<C>: ModulusSize,
+{
+    const KEY_TYPE: &'static str = "EC";
+}
+
 impl<C> crate::key::SerializeJWK for ecdsa::SigningKey<C>
 where
     C: PrimeCurve + CurveArithmetic + JwkParameters,
@@ -153,7 +181,7 @@ where
     FieldBytesSize<C>: ModulusSize,
 {
     fn parameters(&self) -> Vec<(String, serde_json::Value)> {
-        todo!()
+        self.verifying_key().parameters()
     }
 }
 
@@ -223,6 +251,42 @@ where
     }
 }
 
+impl<C> super::VerifyAlgorithm for VerifyingKey<C>
+where
+    C: PrimeCurve + CurveArithmetic + JwkParameters + ecdsa::hazmat::DigestPrimitive,
+    <C as CurveArithmetic>::AffinePoint: VerifyPrimitive<C>,
+    Scalar<C>: Invert<Output = CtOption<Scalar<C>>> + SignPrimitive<C>,
+    SignatureSize<C>: ArrayLength<u8>,
+    MaxSize<C>: ArrayLength<u8>,
+    AffinePoint<C>: FromEncodedPoint<C> + ToEncodedPoint<C>,
+    FieldBytesSize<C>: ModulusSize,
+    VerifyingKey<C>: super::Algorithm<Signature = ecdsa::SignatureBytes<C>>,
+    <FieldBytesSize<C> as Add>::Output: Add<MaxOverhead> + ArrayLength<u8>,
+{
+    type Error = ecdsa::Error;
+    type Key = VerifyingKey<C>;
+
+    fn verify(
+        &self,
+        header: &[u8],
+        payload: &[u8],
+        signature: &[u8],
+    ) -> Result<Self::Signature, Self::Error> {
+        let mut message = BytesMut::with_capacity(header.len() + payload.len() + 1);
+        message.extend_from_slice(header);
+        message.extend_from_slice(b".");
+        message.extend_from_slice(payload);
+
+        let signature = ecdsa::Signature::try_from(signature)?;
+        <Self as Verifier<Signature<C>>>::verify(self, message.as_ref(), &signature)?;
+        Ok(signature.into())
+    }
+
+    fn key(&self) -> &Self::Key {
+        self
+    }
+}
+
 #[cfg(all(test, feature = "p256"))]
 mod test {
 
diff --git a/src/algorithms/hmac.rs b/src/algorithms/hmac.rs
index fd9b616..4315902 100644
--- a/src/algorithms/hmac.rs
+++ b/src/algorithms/hmac.rs
@@ -2,7 +2,7 @@
 //!
 //! Based on the [hmac](https://crates.io/crates/hmac) crate.
 
-use std::convert::Infallible;
+use std::{convert::Infallible, marker::PhantomData};
 
 use base64ct::Encoding;
 use digest::Mac;
@@ -81,7 +81,7 @@ where
     D: digest::Digest + digest::core_api::BlockSizeUser,
 {
     key: HmacKey,
-    digest: hmac::SimpleHmac<D>,
+    _digest: PhantomData<D>,
 }
 
 impl<D> Hmac<D>
@@ -93,8 +93,10 @@ where
     ///
     /// Signing keys are arbitrary bytes.
     pub fn new(key: HmacKey) -> Self {
-        let digest = SimpleHmac::new_from_slice(key.as_ref()).expect("Valid key");
-        Self { key, digest }
+        Self {
+            key,
+            _digest: PhantomData,
+        }
     }
 
     /// Reference to the HMAC key.
@@ -133,8 +135,8 @@ where
 
     fn sign(&self, header: &str, payload: &str) -> Result<Self::Signature, Self::Error> {
         // Create a new, one-shot digest for this signature.
-        let mut digest = self.digest.clone();
-        digest.reset();
+        let mut digest: SimpleHmac<D> =
+            SimpleHmac::new_from_slice(self.key.as_ref()).expect("Valid key");
         let message = format!("{}.{}", header, payload);
         digest.update(message.as_bytes());
         Ok(digest.finalize().into_bytes())
diff --git a/src/algorithms/mod.rs b/src/algorithms/mod.rs
index 8b017e7..aa561ba 100644
--- a/src/algorithms/mod.rs
+++ b/src/algorithms/mod.rs
@@ -69,6 +69,21 @@ pub enum AlgorithmIdentifier {
     None,
 }
 
+impl AlgorithmIdentifier {
+    /// Return whether this algorithm is available for signing.
+    pub fn available(&self) -> bool {
+        match self {
+            Self::None => true,
+
+            Self::HS256 | Self::HS384 | Self::HS512 => cfg!(feature = "hmac"),
+            Self::RS256 | Self::RS384 | Self::RS512 => cfg!(feature = "rsa"),
+            Self::ES256 | Self::ES384 | Self::ES512 => cfg!(feature = "ecdsa"),
+            Self::EdDSA => cfg!(feature = "ed25519"),
+            Self::PS256 | Self::PS384 | Self::PS512 => cfg!(feature = "rsa"),
+        }
+    }
+}
+
 /// A trait to associate an alogritm identifier with an algorithm.
 ///
 /// Algorithm identifiers are used in JWS and JWE to indicate how a token is signed or encrypted.
@@ -118,8 +133,8 @@ pub trait VerifyAlgorithm: Algorithm {
     /// and payload.
     fn verify(
         &self,
-        header: &str,
-        payload: &str,
+        header: &[u8],
+        payload: &[u8],
         signature: &[u8],
     ) -> Result<Self::Signature, Self::Error>;
 
diff --git a/src/algorithms/rsa.rs b/src/algorithms/rsa.rs
index 78e22d2..956f6b1 100644
--- a/src/algorithms/rsa.rs
+++ b/src/algorithms/rsa.rs
@@ -16,7 +16,8 @@
 //! This algorithm is used to sign and verify JSON Web Tokens using the RSASSA-PSS.
 
 use base64ct::{Base64UrlUnpadded, Encoding};
-use rsa::pkcs1v15::SigningKey;
+use bytes::BytesMut;
+use rsa::pkcs1v15::{SigningKey, VerifyingKey};
 use rsa::rand_core::OsRng;
 use rsa::signature::RandomizedSigner;
 use rsa::PublicKeyParts;
@@ -69,6 +70,38 @@ where
     }
 }
 
+impl<D> super::VerifyAlgorithm for VerifyingKey<D>
+where
+    D: digest::Digest,
+    VerifyingKey<D>: super::Algorithm<Signature = rsa::pkcs1v15::Signature>,
+{
+    type Error = signature::Error;
+
+    type Key = rsa::RsaPublicKey;
+
+    fn verify(
+        &self,
+        header: &[u8],
+        payload: &[u8],
+        signature: &[u8],
+    ) -> Result<Self::Signature, Self::Error> {
+        use rsa::signature::Verifier;
+        let signature = rsa::pkcs1v15::Signature::try_from(signature).unwrap();
+
+        let mut message = BytesMut::with_capacity(header.len() + payload.len() + 1);
+        message.extend_from_slice(header);
+        message.extend_from_slice(b".");
+        message.extend_from_slice(payload);
+
+        <Self as Verifier<rsa::pkcs1v15::Signature>>::verify(self, message.as_ref(), &signature)?;
+        Ok(signature)
+    }
+
+    fn key(&self) -> &Self::Key {
+        self.as_ref()
+    }
+}
+
 impl super::Algorithm for RsaPkcs1v15<sha2::Sha256> {
     const IDENTIFIER: super::AlgorithmIdentifier = super::AlgorithmIdentifier::RS256;
     type Signature = rsa::pkcs1v15::Signature;
diff --git a/src/base64data.rs b/src/base64data.rs
index d747358..76ed48f 100644
--- a/src/base64data.rs
+++ b/src/base64data.rs
@@ -120,6 +120,11 @@ where
         let inner = serde_json::to_vec(&self.0)?;
         Ok(base64ct::Base64UrlUnpadded::encode_string(&inner))
     }
+
+    pub(crate) fn serialized_bytes(&self) -> Result<Box<[u8]>, serde_json::Error> {
+        let inner = serde_json::to_vec(&self.0)?;
+        Ok(inner.into_boxed_slice())
+    }
 }
 
 impl<T> AsRef<T> for Base64JSON<T> {
diff --git a/src/jose/derive.rs b/src/jose/derive.rs
index 12ff501..fa1c7bc 100644
--- a/src/jose/derive.rs
+++ b/src/jose/derive.rs
@@ -106,6 +106,13 @@ where
             KeyDerivation::Explicit(value) => DerivedKeyValue::Explicit(value),
         }
     }
+
+    pub(super) fn explicit(value: Option<Builder::Value>) -> Self {
+        match value {
+            Some(value) => DerivedKeyValue::Explicit(value),
+            None => DerivedKeyValue::Omit,
+        }
+    }
 }
 
 impl<Builder, Key> ser::Serialize for DerivedKeyValue<Builder, Key>
diff --git a/src/jose/mod.rs b/src/jose/mod.rs
index 74b88d8..cf227ba 100644
--- a/src/jose/mod.rs
+++ b/src/jose/mod.rs
@@ -18,6 +18,7 @@ use url::Url;
 
 #[cfg(feature = "fmt")]
 use crate::base64data::Base64JSON;
+use crate::token::TokenVerifyingError;
 use crate::{algorithms::AlgorithmIdentifier, key::SerializeJWK};
 
 #[cfg(feature = "fmt")]
@@ -108,7 +109,7 @@ const REGISTERED_HEADER_KEYS: [&str; 11] = [
 #[non_exhaustive]
 pub struct Header<H, State> {
     #[serde(flatten)]
-    state: State,
+    pub(crate) state: State,
 
     /// The set of registered header parameters from [JWS][] and [JWA][].
     ///
@@ -207,8 +208,17 @@ where
     /// Render a signed JWK header into its rendered
     /// form, where the derived fields have been built
     /// as necessary.
-    pub fn render(self) -> Header<H, RenderedHeader> {
+    pub fn render(self) -> Header<H, RenderedHeader>
+    where
+        H: Serialize,
+        SignedHeader<Key>: HeaderState,
+    {
+        let headers = Base64JSON(&self)
+            .serialized_bytes()
+            .expect("valid header value");
+
         let state = RenderedHeader {
+            raw: headers,
             algorithm: self.state.algorithm,
             key: self.state.key.build(),
             thumbprint: self.state.thumbprint.build(),
@@ -229,11 +239,30 @@ impl<H> Header<H, RenderedHeader> {
     }
 
     #[allow(unused_variables)]
-    pub(crate) fn verify<A>(self, key: &A::Key) -> Result<Header<H, SignedHeader<A::Key>>, A::Error>
+    pub(crate) fn verify<A>(
+        self,
+        key: &A::Key,
+    ) -> Result<Header<H, SignedHeader<A::Key>>, TokenVerifyingError<A::Error>>
     where
         A: crate::algorithms::VerifyAlgorithm,
     {
-        todo!("verify");
+        // This may need to only verify that the algorithm header matches the key algorithm.
+        if A::IDENTIFIER != self.state.algorithm {
+            return Err(TokenVerifyingError::Algorithm(
+                A::IDENTIFIER,
+                self.state.algorithm,
+            ));
+        }
+        Ok(Header {
+            state: SignedHeader {
+                algorithm: self.state.algorithm,
+                key: DerivedKeyValue::explicit(self.state.key),
+                thumbprint: DerivedKeyValue::explicit(self.state.thumbprint),
+                thumbprint_sha256: DerivedKeyValue::explicit(self.state.thumbprint_sha256),
+            },
+            registered: self.registered,
+            custom: self.custom,
+        })
     }
 }
 
diff --git a/src/jose/rendered.rs b/src/jose/rendered.rs
index 9f177d9..7bdc09b 100644
--- a/src/jose/rendered.rs
+++ b/src/jose/rendered.rs
@@ -15,6 +15,9 @@ use super::HeaderState;
 /// and not thd derivation, so the fields may be in inconsistent states.
 #[derive(Debug, Clone, Serialize, Deserialize)]
 pub struct RenderedHeader {
+    /// The raw bytes of the header, as it was signed.
+    pub(crate) raw: Box<[u8]>,
+
     #[doc = include_str!(concat!(env!("CARGO_MANIFEST_DIR"), "/docs/jose/algorithm.md"))]
     #[serde(rename = "alg")]
     pub(super) algorithm: AlgorithmIdentifier,
diff --git a/src/token/mod.rs b/src/token/mod.rs
index 8b004ac..c582d8e 100644
--- a/src/token/mod.rs
+++ b/src/token/mod.rs
@@ -67,6 +67,13 @@ where
             Payload::Empty => Ok("".to_owned()),
         }
     }
+
+    fn serialized_bytes(&self) -> Result<Box<[u8]>, serde_json::Error> {
+        match self {
+            Payload::Json(data) => data.serialized_bytes(),
+            Payload::Empty => Ok(Box::new([])),
+        }
+    }
 }
 
 impl<P> From<P> for Payload<P> {
@@ -364,16 +371,16 @@ where
         }
 
         let signature = &self.state.signature;
-        let header = self
-            .state
-            .header
-            .verify::<A>(algorithm.key())
-            .map_err(TokenVerifyingError::Verify)?;
-        let headers = Base64JSON(&header).serialized_value()?;
-        let payload = self.payload.serialized_value()?;
         let signature = algorithm
-            .verify(&headers, &payload, signature.as_ref())
+            .verify(
+                &self.state.header.state.raw,
+                &self.state.payload,
+                signature.as_ref(),
+            )
             .map_err(TokenVerifyingError::Verify)?;
+
+        let header = self.state.header.verify::<A>(algorithm.key())?;
+
         Ok(Token {
             payload: self.payload,
             state: Verified { header, signature },
@@ -386,15 +393,23 @@ impl<P, H, Alg, Fmt> Token<P, Signed<H, Alg>, Fmt>
 where
     Fmt: TokenFormat,
     Alg: SigningAlgorithm,
+    Alg::Key: Clone,
+    H: Serialize,
+    P: Serialize,
 {
     /// Transition the token back into an unverified state.
     ///
     /// This method consumes the token and returns a new one, which still includes the signature
     /// but which is no longer considered verified.
     pub fn unverify(self) -> Token<P, Unverified<H>, Fmt> {
+        let payload = self
+            .payload
+            .serialized_bytes()
+            .expect("valid payload bytes");
         Token {
             payload: self.payload,
             state: Unverified {
+                payload,
                 header: self.state.header.render(),
                 signature: Base64Data(self.state.signature.as_ref().to_owned().into()),
             },
@@ -408,7 +423,7 @@ impl<P, S, Fmt> fmt::JWTFormat for Token<P, S, Fmt>
 where
     S: HasSignature,
     <S as MaybeSigned>::Header: Serialize,
-    <S as MaybeSigned>::HeaderState: Serialize + HeaderState,
+    <S as MaybeSigned>::HeaderState: HeaderState,
     P: Serialize,
     Fmt: TokenFormat,
 {
diff --git a/src/token/state.rs b/src/token/state.rs
index 9b1db01..6bb1e9c 100644
--- a/src/token/state.rs
+++ b/src/token/state.rs
@@ -189,6 +189,7 @@ where
     deserialize = "H: for<'deh> Deserialize<'deh>"
 ))]
 pub struct Unverified<H> {
+    pub(super) payload: Box<[u8]>,
     pub(super) header: jose::Header<H, jose::RenderedHeader>,
     pub(super) signature: Base64Data<SignatureBytes>,
 }