diff --git a/draft-ietf-quic-http.md b/draft-ietf-quic-http.md
index de6cc9a852..b5d5edb891 100644
--- a/draft-ietf-quic-http.md
+++ b/draft-ietf-quic-http.md
@@ -316,10 +316,21 @@ authoritative server for an HTTP URL is discussed in Section 4.3 of
 
 The "https" scheme associates authority with possession of a certificate that
 the client considers to be trustworthy for the host identified by the authority
-component of the URL. If a server presents a certificate and proof that it
-controls the corresponding private key, then a client will accept a secured
-TLS session with that server as being authoritative for all origins with the
-"https" scheme and a host identified in the certificate.
+component of the URL.
+
+If a server presents a valid certificate and proof that it controls the
+corresponding private key, then a client will accept a secured TLS session with
+that server as being authoritative for all origins with the "https" scheme and a
+host identified in the certificate.  The host must be listed either as the CN
+field of the certificate subject or as a dNSName in the subjectAltName field of
+the certificate; see {{!RFC6125}}.  For a host that is an IP address, the client
+MUST verify that the address appears as an iPAddress in the subjectAltName field
+of the certificate.
+
+If the hostname or address is not present in the certificate, the client MUST
+NOT consider the server authoritative for origins containing that hostname or
+address.  See Section 4.3 of {{!SEMANTICS}} for more detail on authoritative
+access.
 
 A client MAY attempt access to a resource with an "https" URI by resolving the
 host identifier to an IP address, establishing a QUIC connection to that address
@@ -404,23 +415,12 @@ example, when a user navigates away from a particular web page) or until the
 server closes the connection.
 
 Once a connection exists to a server endpoint, this connection MAY be reused for
-requests with multiple different URI authority components.  In general, a server
-is considered authoritative for all URIs with the "https" scheme for which the
-hostname in the URI is present in the authenticated certificate provided by the
-server, either as the CN field of the certificate subject or as a dNSName in the
-subjectAltName field of the certificate; see {{!RFC6125}}.  For a host that is
-an IP address, the client MUST verify that the address appears as an iPAddress
-in the subjectAltName field of the certificate.  If the hostname or address is
-not present in the certificate, the client MUST NOT consider the server
-authoritative for origins containing that hostname or address.  See Section 4.3
-of {{!SEMANTICS}} for more detail on authoritative access.
-
-Clients SHOULD NOT open more than one HTTP/3 connection to a given host and port
-pair, where the host is derived from a URI, a selected alternative service
-({{!ALTSVC}}), or a configured proxy.  A client MAY open multiple HTTP/3
-connections to the same IP address and UDP port using different transport or TLS
-configurations but SHOULD avoid creating multiple connections with the same
-configuration.
+requests with multiple different URI authority components.  Clients SHOULD NOT
+open more than one HTTP/3 connection to a given host and port pair, where the
+host is derived from a URI, a selected alternative service ({{!ALTSVC}}), or a
+configured proxy.  A client MAY open multiple HTTP/3 connections to the same IP
+address and UDP port using different transport or TLS configurations but SHOULD
+avoid creating multiple connections with the same configuration.
 
 Servers are encouraged to maintain open HTTP/3 connections for as long as
 possible but are permitted to terminate idle connections if necessary.  When