diff --git a/rcgen/src/certificate.rs b/rcgen/src/certificate.rs
index 9c12b802..aaba70de 100644
--- a/rcgen/src/certificate.rs
+++ b/rcgen/src/certificate.rs
@@ -198,11 +198,11 @@ impl CertificateParams {
 	/// for the presence of the `BasicConstraints` extension, or perform any other
 	/// validation.
 	///
-	/// You can use [`rustls_pemfile::certs`] to get the `ca_cert` input. If
-	/// you have already a byte slice, just calling `into()` and taking a reference
-	/// will convert it to [`CertificateDer`].
+	/// [`rustls_pemfile::certs()`] is often used to obtain a [`CertificateDer`] from PEM input.
+	/// If you already have a byte slice containing DER, it can trivially be converted into
+	/// [`CertificateDer`] using the [`Into`] trait.
 	///
-	/// [`rustls_pemfile::certs`]: https://docs.rs/rustls-pemfile/latest/rustls_pemfile/fn.certs.html
+	/// [`rustls_pemfile::certs()`]: https://docs.rs/rustls-pemfile/latest/rustls_pemfile/fn.certs.html
 	#[cfg(feature = "x509-parser")]
 	pub fn from_ca_cert_der(ca_cert: &CertificateDer<'_>) -> Result<Self, Error> {
 		let (_remainder, x509) = x509_parser::parse_x509_certificate(ca_cert)
diff --git a/rcgen/src/csr.rs b/rcgen/src/csr.rs
index 1f0be614..61f1e223 100644
--- a/rcgen/src/csr.rs
+++ b/rcgen/src/csr.rs
@@ -71,11 +71,11 @@ impl CertificateSigningRequestParams {
 	/// Currently, this only supports the `Subject Alternative Name` extension.
 	/// On encountering other extensions, this function will return an error.
 	///
-	/// You can use [`rustls_pemfile::csr`] to get the `csr` input. If
-	/// you have already a byte slice, just calling `into()` and taking a reference
-	/// will convert it to [`CertificateSigningRequestDer`].
+	/// [`rustls_pemfile::csr()`] is often used to obtain a [`CertificateSigningRequestDer`] from
+	/// PEM input. If you already have a byte slice containing DER, it can trivially be converted
+	/// into [`CertificateSigningRequestDer`] using the [`Into`] trait.
 	///
-	/// [`rustls_pemfile::csr`]: https://docs.rs/rustls-pemfile/latest/rustls_pemfile/fn.csr.html
+	/// [`rustls_pemfile::csr()`]: https://docs.rs/rustls-pemfile/latest/rustls_pemfile/fn.csr.html
 	#[cfg(feature = "x509-parser")]
 	pub fn from_der(csr: &CertificateSigningRequestDer<'_>) -> Result<Self, Error> {
 		use x509_parser::prelude::FromDer;
diff --git a/rcgen/src/key_pair.rs b/rcgen/src/key_pair.rs
index 3fc8b924..ace1084f 100644
--- a/rcgen/src/key_pair.rs
+++ b/rcgen/src/key_pair.rs
@@ -202,16 +202,18 @@ impl KeyPair {
 
 	/// Obtains the key pair from a DER formatted key using the specified [`SignatureAlgorithm`]
 	///
-	/// You can use [`rustls_pemfile::private_key`] to get the `pkcs8` input. If
-	/// you have already a byte slice, just calling `into()` and taking a reference
-	/// will convert it to a [`PrivatePkcs8KeyDer`].
-	///
 	/// If you have a [`PrivatePkcs8KeyDer`], you can usually rely on the [`TryFrom`] implementation
 	/// to obtain a [`KeyPair`] -- it will determine the correct [`SignatureAlgorithm`] for you.
 	/// However, sometimes multiple signature algorithms fit for the same DER key. In those instances,
 	/// you can use this function to precisely specify the `SignatureAlgorithm`.
 	///
-	/// [`rustls_pemfile::private_key`]: https://docs.rs/rustls-pemfile/latest/rustls_pemfile/fn.private_key.html
+	/// [`rustls_pemfile::private_key()`] is often used to obtain a [`PrivateKeyDer`] from PEM
+	/// input. If the obtained [`PrivateKeyDer`] is a `Pkcs8` variant, you can use its contents
+	/// as input for this function. Alternatively, if you already have a byte slice containing DER,
+	/// it can trivially be converted into [`PrivatePkcs8KeyDer`] using the [`Into`] trait.
+	///
+	/// [`rustls_pemfile::private_key()`]: https://docs.rs/rustls-pemfile/latest/rustls_pemfile/fn.private_key.html
+	/// [`PrivateKeyDer`]: https://docs.rs/rustls-pki-types/latest/rustls_pki_types/enum.PrivateKeyDer.html
 	#[cfg(feature = "crypto")]
 	pub fn from_der_and_sign_algo(
 		pkcs8: &PrivatePkcs8KeyDer<'_>,
@@ -259,11 +261,13 @@ impl KeyPair {
 
 	/// Parses the key pair from the DER format
 	///
-	/// You can use [`rustls_pemfile::private_key`] to get the `pkcs8` input. If
-	/// you have already a byte slice, just calling `into()` and taking a reference
-	/// will convert it to a [`PrivatePkcs8KeyDer`].
+	/// [`rustls_pemfile::private_key()`] is often used to obtain a [`PrivateKeyDer`] from PEM
+	/// input. If the obtained [`PrivateKeyDer`] is a `Pkcs8` variant, you can use its contents
+	/// as input for this function. Alternatively, if you already have a byte slice containing DER,
+	/// it can trivially be converted into [`PrivatePkcs8KeyDer`] using the [`Into`] trait.
 	///
-	/// [`rustls_pemfile::private_key`]: https://docs.rs/rustls-pemfile/latest/rustls_pemfile/fn.private_key.html
+	/// [`rustls_pemfile::private_key()`]: https://docs.rs/rustls-pemfile/latest/rustls_pemfile/fn.private_key.html
+	/// [`PrivateKeyDer`]: https://docs.rs/rustls-pki-types/latest/rustls_pki_types/enum.PrivateKeyDer.html
 	#[cfg(feature = "crypto")]
 	pub(crate) fn from_raw(
 		pkcs8: &PrivatePkcs8KeyDer,