diff --git a/rcgen/src/certificate.rs b/rcgen/src/certificate.rs
index e34abd3f..ce34495e 100644
--- a/rcgen/src/certificate.rs
+++ b/rcgen/src/certificate.rs
@@ -634,21 +634,19 @@ fn write_general_subtrees(writer: DERWriter, tag: u64, general_subtrees: &[Gener
 		writer.write_sequence(|writer| {
 			for subtree in general_subtrees.iter() {
 				writer.next().write_sequence(|writer| {
-					writer
-						.next()
-						.write_tagged_implicit(
-							Tag::context(subtree.tag()),
-							|writer| match subtree {
-								GeneralSubtree::Rfc822Name(name)
-								| GeneralSubtree::DnsName(name) => writer.write_ia5_string(name),
-								GeneralSubtree::DirectoryName(name) => {
-									write_distinguished_name(writer, name)
-								},
-								GeneralSubtree::IpAddress(subnet) => {
-									writer.write_bytes(&subnet.to_bytes())
-								},
-							},
-						);
+					let writer = writer.next();
+					let tag = Tag::context(subtree.tag());
+					match subtree {
+						GeneralSubtree::Rfc822Name(name) | GeneralSubtree::DnsName(name) => writer
+							.write_tagged_implicit(tag, |writer| writer.write_ia5_string(name)),
+						// `Name` is a CHOICE, so X.680 §31.2.7 requires explicit tagging.
+						GeneralSubtree::DirectoryName(name) => writer
+							.write_tagged(tag, |writer| write_distinguished_name(writer, name)),
+						GeneralSubtree::IpAddress(subnet) => writer
+							.write_tagged_implicit(tag, |writer| {
+								writer.write_bytes(&subnet.to_bytes())
+							}),
+					}
 					// minimum must be 0 (the default) and maximum must be absent
 				});
 			}
diff --git a/verify-tests/tests/openssl.rs b/verify-tests/tests/openssl.rs
index a99cad49..bf736794 100644
--- a/verify-tests/tests/openssl.rs
+++ b/verify-tests/tests/openssl.rs
@@ -12,8 +12,8 @@ use openssl::stack::Stack;
 use openssl::x509::store::{X509Store, X509StoreBuilder};
 use openssl::x509::{CrlStatus, X509Crl, X509Req, X509StoreContext, X509};
 use rcgen::{
-	BasicConstraints, Certificate, CertificateParams, DnType, DnValue, GeneralSubtree, IsCa,
-	Issuer, KeyPair, NameConstraints,
+	BasicConstraints, Certificate, CertificateParams, DistinguishedName, DnType, DnValue,
+	GeneralSubtree, IsCa, Issuer, KeyPair, NameConstraints,
 };
 use verify_tests as util;
 
@@ -404,6 +404,39 @@ fn test_openssl_separate_ca_name_constraints() {
 	verify_cert_ca(&cert.pem(), &key, &ca_cert.pem());
 }
 
+#[test]
+fn test_openssl_separate_ca_name_constraints_directory_name() {
+	let (mut ca_params, ca_key) = util::default_params();
+	ca_params.is_ca = IsCa::Ca(BasicConstraints::Unconstrained);
+
+	let mut permitted = DistinguishedName::new();
+	permitted.push(DnType::OrganizationName, "Crab widgits SE");
+
+	ca_params.name_constraints = Some(NameConstraints {
+		permitted_subtrees: vec![
+			GeneralSubtree::DnsName("crabs.crabs".to_string()),
+			GeneralSubtree::DirectoryName(permitted),
+		],
+		excluded_subtrees: Vec::new(),
+	});
+	let ca_cert = ca_params.self_signed(&ca_key).unwrap();
+	let ca = Issuer::new(ca_params, ca_key);
+
+	let mut params = CertificateParams::new(vec!["crabs.crabs".to_string()]).unwrap();
+	params.distinguished_name = DistinguishedName::new();
+	params
+		.distinguished_name
+		.push(DnType::OrganizationName, "Crab widgits SE");
+	params
+		.distinguished_name
+		.push(DnType::CommonName, "Dev domain");
+	let cert_key = KeyPair::generate().unwrap();
+	let cert = params.signed_by(&cert_key, &ca).unwrap();
+	let key = cert_key.serialize_der();
+
+	verify_cert_ca(&cert.pem(), &key, &ca_cert.pem());
+}
+
 #[test]
 fn test_openssl_crl_parse() {
 	// Create a CRL with one revoked cert, and an issuer to sign the CRL.