diff --git a/src/resolve/resolved-dnstls-openssl.c b/src/resolve/resolved-dnstls-openssl.c
index 5dd7737337..a7a8b1152a 100644
--- a/src/resolve/resolved-dnstls-openssl.c
+++ b/src/resolve/resolved-dnstls-openssl.c
@@ -46,11 +46,9 @@ static int dnstls_flush_write_buffer(DnsStream *stream) {
 }
 
 int dnstls_stream_connect_tls(DnsStream *stream, DnsServer *server) {
+        _cleanup_(BIO_freep) BIO *rb = NULL, *wb = NULL;
         _cleanup_(SSL_freep) SSL *s = NULL;
-        _cleanup_(BIO_freep) BIO *rb = NULL;
-        _cleanup_(BIO_freep) BIO *wb = NULL;
-        int r;
-        int error;
+        int error, r;
 
         assert(stream);
         assert(server);
@@ -73,6 +71,7 @@ int dnstls_stream_connect_tls(DnsStream *stream, DnsServer *server) {
         SSL_set_session(s, server->dnstls_data.session);
         SSL_set_bio(s, TAKE_PTR(rb), TAKE_PTR(wb));
 
+        ERR_clear_error();
         stream->dnstls_data.handshake = SSL_do_handshake(s);
         if (stream->dnstls_data.handshake <= 0) {
                 error = SSL_get_error(s, stream->dnstls_data.handshake);
@@ -105,14 +104,13 @@ void dnstls_stream_free(DnsStream *stream) {
 }
 
 int dnstls_stream_on_io(DnsStream *stream, uint32_t revents) {
-        int r;
-        int error;
+        int error, r;
 
         assert(stream);
         assert(stream->encrypted);
         assert(stream->dnstls_data.ssl);
 
-        /* Flush write buffer when requested by OpenSSL ss*/
+        /* Flush write buffer when requested by OpenSSL */
         if ((revents & EPOLLOUT) && (stream->dnstls_events & EPOLLOUT)) {
                 r = dnstls_flush_write_buffer(stream);
                 if (r < 0)
@@ -120,35 +118,48 @@ int dnstls_stream_on_io(DnsStream *stream, uint32_t revents) {
         }
 
         if (stream->dnstls_data.shutdown) {
+                ERR_clear_error();
                 r = SSL_shutdown(stream->dnstls_data.ssl);
-                if (r <= 0) {
+                if (r == 0) {
+                        stream->dnstls_events = 0;
+
+                        r = dnstls_flush_write_buffer(stream);
+                        if (r < 0)
+                                return r;
+
+                        return -EAGAIN;
+                } else if (r < 0) {
                         error = SSL_get_error(stream->dnstls_data.ssl, r);
-                        if (r == 0 || IN_SET(error, SSL_ERROR_WANT_READ, SSL_ERROR_WANT_WRITE)) {
-                                if (r < 0)
-                                        stream->dnstls_events = error == SSL_ERROR_WANT_READ ? EPOLLIN : EPOLLOUT;
+                        if (IN_SET(error, SSL_ERROR_WANT_READ, SSL_ERROR_WANT_WRITE)) {
+                                stream->dnstls_events = error == SSL_ERROR_WANT_READ ? EPOLLIN : EPOLLOUT;
 
                                 r = dnstls_flush_write_buffer(stream);
                                 if (r < 0)
                                         return r;
 
                                 return -EAGAIN;
+                        } else if (error == SSL_ERROR_SYSCALL) {
+                                if (errno > 0)
+                                        log_debug_errno(errno, "Failed to invoke SSL_shutdown, ignoring: %m");
                         } else {
                                 char errbuf[256];
 
                                 ERR_error_string_n(error, errbuf, sizeof(errbuf));
-                                log_debug("Failed to invoke SSL_shutdown: %s", errbuf);
+                                log_debug("Failed to invoke SSL_shutdown, ignoring: %s", errbuf);
                         }
                 }
 
+                stream->dnstls_events = 0;
+                stream->dnstls_data.shutdown = false;
+
                 r = dnstls_flush_write_buffer(stream);
                 if (r < 0)
                         return r;
 
-                stream->dnstls_events = 0;
-                stream->dnstls_data.shutdown = false;
                 dns_stream_unref(stream);
                 return DNSTLS_STREAM_CLOSED;
         } else if (stream->dnstls_data.handshake <= 0) {
+                ERR_clear_error();
                 stream->dnstls_data.handshake = SSL_do_handshake(stream->dnstls_data.ssl);
                 if (stream->dnstls_data.handshake <= 0) {
                         error = SSL_get_error(stream->dnstls_data.ssl, stream->dnstls_data.handshake);
@@ -178,8 +189,7 @@ int dnstls_stream_on_io(DnsStream *stream, uint32_t revents) {
 }
 
 int dnstls_stream_shutdown(DnsStream *stream, int error) {
-        int r;
-        int ssl_error;
+        int ssl_error, r;
         SSL_SESSION *s;
 
         assert(stream);
@@ -197,6 +207,7 @@ int dnstls_stream_shutdown(DnsStream *stream, int error) {
         }
 
         if (error == ETIMEDOUT) {
+                ERR_clear_error();
                 r = SSL_shutdown(stream->dnstls_data.ssl);
                 if (r == 0) {
                         if (!stream->dnstls_data.shutdown) {
@@ -204,6 +215,8 @@ int dnstls_stream_shutdown(DnsStream *stream, int error) {
                                 dns_stream_ref(stream);
                         }
 
+                        stream->dnstls_events = 0;
+
                         r = dnstls_flush_write_buffer(stream);
                         if (r < 0)
                                 return r;
@@ -222,11 +235,14 @@ int dnstls_stream_shutdown(DnsStream *stream, int error) {
                                         dns_stream_ref(stream);
                                 }
                                 return -EAGAIN;
+                        } else if (ssl_error == SSL_ERROR_SYSCALL) {
+                                if (errno > 0)
+                                        log_debug_errno(errno, "Failed to invoke SSL_shutdown, ignoring: %m");
                         } else {
                                 char errbuf[256];
 
                                 ERR_error_string_n(ssl_error, errbuf, sizeof(errbuf));
-                                log_debug("Failed to invoke SSL_shutdown: %s", errbuf);
+                                log_debug("Failed to invoke SSL_shutdown, ignoring: %s", errbuf);
                         }
                 }
 
@@ -240,8 +256,7 @@ int dnstls_stream_shutdown(DnsStream *stream, int error) {
 }
 
 ssize_t dnstls_stream_write(DnsStream *stream, const char *buf, size_t count) {
-        int r;
-        int error;
+        int error, r;
         ssize_t ss;
 
         assert(stream);
@@ -249,26 +264,27 @@ ssize_t dnstls_stream_write(DnsStream *stream, const char *buf, size_t count) {
         assert(stream->dnstls_data.ssl);
         assert(buf);
 
+        ERR_clear_error();
         ss = r = SSL_write(stream->dnstls_data.ssl, buf, count);
         if (r <= 0) {
-                error = SSL_get_error(stream->dnstls_data.ssl, ss);
+                error = SSL_get_error(stream->dnstls_data.ssl, r);
                 if (IN_SET(error, SSL_ERROR_WANT_READ, SSL_ERROR_WANT_WRITE)) {
                         stream->dnstls_events = error == SSL_ERROR_WANT_READ ? EPOLLIN : EPOLLOUT;
-                        r = dnstls_flush_write_buffer(stream);
-                        if (r < 0)
-                                return r;
-
                         ss = -EAGAIN;
+                } else if (error == SSL_ERROR_ZERO_RETURN) {
+                        stream->dnstls_events = 0;
+                        ss = 0;
                 } else {
                         char errbuf[256];
 
                         ERR_error_string_n(error, errbuf, sizeof(errbuf));
-                        log_debug("Failed to invoke SSL_read: %s", errbuf);
+                        log_debug("Failed to invoke SSL_write: %s", errbuf);
+                        stream->dnstls_events = 0;
                         ss = -EPIPE;
                 }
-        }
+        } else
+                stream->dnstls_events = 0;
 
-        stream->dnstls_events = 0;
         r = dnstls_flush_write_buffer(stream);
         if (r < 0)
                 return r;
@@ -277,8 +293,7 @@ ssize_t dnstls_stream_write(DnsStream *stream, const char *buf, size_t count) {
 }
 
 ssize_t dnstls_stream_read(DnsStream *stream, void *buf, size_t count) {
-        int r;
-        int error;
+        int error, r;
         ssize_t ss;
 
         assert(stream);
@@ -286,28 +301,26 @@ ssize_t dnstls_stream_read(DnsStream *stream, void *buf, size_t count) {
         assert(stream->dnstls_data.ssl);
         assert(buf);
 
+        ERR_clear_error();
         ss = r = SSL_read(stream->dnstls_data.ssl, buf, count);
         if (r <= 0) {
-                error = SSL_get_error(stream->dnstls_data.ssl, ss);
+                error = SSL_get_error(stream->dnstls_data.ssl, r);
                 if (IN_SET(error, SSL_ERROR_WANT_READ, SSL_ERROR_WANT_WRITE)) {
                         stream->dnstls_events = error == SSL_ERROR_WANT_READ ? EPOLLIN : EPOLLOUT;
-
-                        /* flush write buffer in cache of renegotiation */
-                        r = dnstls_flush_write_buffer(stream);
-                        if (r < 0)
-                                return r;
-
                         ss = -EAGAIN;
+                } else if (error == SSL_ERROR_ZERO_RETURN) {
+                        stream->dnstls_events = 0;
+                        ss = 0;
                 } else {
                         char errbuf[256];
 
                         ERR_error_string_n(error, errbuf, sizeof(errbuf));
                         log_debug("Failed to invoke SSL_read: %s", errbuf);
+                        stream->dnstls_events = 0;
                         ss = -EPIPE;
                 }
-        }
-
-        stream->dnstls_events = 0;
+        } else
+                stream->dnstls_events = 0;
 
         /* flush write buffer in cache of renegotiation */
         r = dnstls_flush_write_buffer(stream);