diff --git a/gnutls-dtls.c b/gnutls-dtls.c
index 3f1a4dcf..c6c716e4 100644
--- a/gnutls-dtls.c
+++ b/gnutls-dtls.c
@@ -317,6 +317,48 @@ static int start_dtls_resume_handshake(struct openconnect_info *vpninfo, gnutls_
 	return 0;
 }
 
+/*
+ * GnuTLS version between 3.6.3 and 3.6.12 send zero'ed ClientHello. Make sure
+ * we are not hitting that bug. Adapted from:
+ * https://gitlab.com/gnutls/gnutls/-/blob/3.6.13/tests/tls_hello_random_value.c
+ */
+static int check_client_hello_random(gnutls_session_t ttls_sess, unsigned int type,
+				     unsigned hook, unsigned int incoming, const gnutls_datum_t *msg)
+{
+	unsigned non_zero = 0, i;
+	struct openconnect_info *vpninfo = (struct openconnect_info *)gnutls_session_get_ptr(ttls_sess);
+
+	if (type == GNUTLS_HANDSHAKE_CLIENT_HELLO && hook == GNUTLS_HOOK_POST) {
+		gnutls_datum_t buf;
+		gnutls_session_get_random(ttls_sess, &buf, NULL);
+		if (buf.size != 32) {
+			vpn_progress(vpninfo, PRG_ERR,
+				     _("GnuTLS used %d ClientHello random bytes; this should never happen\n"),
+				     buf.size);
+			return GNUTLS_E_INVALID_REQUEST;
+		}
+
+		for (i = 0; i < buf.size; ++i) {
+			if (buf.data[i] != 0) {
+				non_zero++;
+			}
+		}
+
+		/* The GnuTLS bug was that *all* bytes were zero, but as part of the unit test
+		 * they also slipped in a coincidental check on how well the random number
+		 * generator is behaving. Eight or more zeroes is a bad thing whatever the
+		 * reason for it. So we have the same check. */
+		if (non_zero <= 8) {
+			/* TODO: mention CVE number in log message once it's assigned */
+			vpn_progress(vpninfo, PRG_ERR,
+			     _("GnuTLS sent insecure ClientHello random. Upgrade to 3.6.13 or newer.\n"));
+			return GNUTLS_E_INVALID_REQUEST;
+		}
+	}
+
+	return 0;
+}
+
 int start_dtls_handshake(struct openconnect_info *vpninfo, int dtls_fd)
 {
 	gnutls_session_t dtls_ssl;
@@ -333,20 +375,24 @@ int start_dtls_handshake(struct openconnect_info *vpninfo, int dtls_fd)
 	gnutls_transport_set_ptr(dtls_ssl,
 				 (gnutls_transport_ptr_t)(intptr_t)dtls_fd);
 
-
 	if (!strcmp(vpninfo->dtls_cipher, "PSK-NEGOTIATE"))
 		ret = start_dtls_psk_handshake(vpninfo, dtls_ssl);
 	else
 		ret = start_dtls_resume_handshake(vpninfo, dtls_ssl);
 
 	if (ret) {
-	fail:
 		if (ret != -EAGAIN)
 			vpninfo->dtls_attempt_period = 0;
 		gnutls_deinit(dtls_ssl);
 		return ret;
 	}
 
+	if (gnutls_check_version_numeric(3,6,3) && !gnutls_check_version_numeric(3,6,13)) {
+		gnutls_handshake_set_hook_function(dtls_ssl, GNUTLS_HANDSHAKE_CLIENT_HELLO,
+						   GNUTLS_HOOK_POST, check_client_hello_random);
+	}
+
+
 	vpninfo->dtls_ssl = dtls_ssl;
 	return 0;
 }
diff --git a/gnutls.c b/gnutls.c
index 34c397b7..1098cc55 100644
--- a/gnutls.c
+++ b/gnutls.c
@@ -2241,15 +2241,6 @@ int openconnect_open_https(struct openconnect_info *vpninfo)
 				     GNUTLS_DEFAULT_HANDSHAKE_TIMEOUT);
 #endif
 
-#ifdef HAVE_DTLS
-	if (vpninfo->dtls_state != DTLS_DISABLED && vpninfo->proto->udp_setup == dtls_setup &&
-	    gnutls_check_version_numeric(3,6,3) && !gnutls_check_version_numeric(3,6,13)) {
-		vpn_progress(vpninfo, PRG_ERR,
-			     _("Disabling DTLS: This version of the GnuTLS library has an insecure DTLS implementation.\n"));
-		vpninfo->dtls_state = DTLS_DISABLED;
-	}
-#endif
-
 	err = cstp_handshake(vpninfo, 1);
 	if (err)
 		return err;
diff --git a/www/changelog.xml b/www/changelog.xml
index 496d0bf1..2d2dc070 100644
--- a/www/changelog.xml
+++ b/www/changelog.xml
@@ -16,7 +16,7 @@
    <li><b>OpenConnect HEAD</b>
      <ul>
        <li>Don't abort Pulse connection when server-provided certificate MD5 doesn't match.</li>
-       <li>Fix off-by-one in check for bad GnuTLS versions, and add build time check.</li>
+       <li>Fix off-by-one in check for bad GnuTLS versions, and add build and run time checks.</li>
      </ul><br/>
   </li>
   <li><b><a href="ftp://ftp.infradead.org/pub/openconnect/openconnect-8.06.tar.gz">OpenConnect v8.06</a></b>