diff --git a/bin/varnishd/VSC_main.vsc b/bin/varnishd/VSC_main.vsc
index a2e2d01437..dbcbcdf659 100644
--- a/bin/varnishd/VSC_main.vsc
+++ b/bin/varnishd/VSC_main.vsc
@@ -33,9 +33,46 @@
 .. varnish_vsc:: sess_fail
 	:oneliner:	Session accept failures
 
-	Count of failures to accept TCP connection.  Either the client
-	changed its mind, or the kernel ran out of some resource like file
-	descriptors.
+	Count of failures to accept TCP connection.
+
+	This counter is the sum of the sess_fail_* counters, which
+	give more detailled information.
+
+.. varnish_vsc:: sess_fail_econnaborted
+	:oneliner:	Session accept failures: connection aborted
+
+	Detailled reason for sess_fail: Connection aborted by the
+	client, usually harmless.
+
+.. varnish_vsc:: sess_fail_eintr
+	:oneliner:	Session accept failures: interrupted system call
+
+	Detailled reason for sess_fail: The accept() call was
+	interrupted, usually harmless
+
+.. varnish_vsc:: sess_fail_emfile
+	:oneliner:	Session accept failures: too many open files
+
+	Detailled reason for sess_fail: No file descriptor was
+	available. Consider raising RLIMIT_NOFILE (see ulimit -n).
+
+.. varnish_vsc:: sess_fail_ebadf
+	:oneliner:	Session accept failures: bad file descriptor
+
+	Detailled reason for sess_fail: The listen socket file
+	descriptor was invalid. Should never happen.
+
+.. varnish_vsc:: sess_fail_enomem
+	:oneliner:	Session accept failures: not enough memory
+
+	Detailled reason for sess_fail: Most likely insufficient
+	socket buffer memory. Should never happen
+
+.. varnish_vsc:: sess_fail_other
+	:oneliner:	Session accept failures: other
+
+	Detailled reason for sess_fail: neither of the above, see
+	Debug log (varnishlog -g raw -I Debug:^Accept).
 
 .. varnish_vsc:: client_req_400
 	:oneliner:	Client requests received, subject to 400 errors
diff --git a/bin/varnishd/cache/cache_acceptor.c b/bin/varnishd/cache/cache_acceptor.c
index 6973d01d8b..455697fe1f 100644
--- a/bin/varnishd/cache/cache_acceptor.c
+++ b/bin/varnishd/cache/cache_acceptor.c
@@ -489,23 +489,32 @@ vca_accept_task(struct worker *wrk, void *arg)
 		if (i < 0) {
 			switch (errno) {
 			case ECONNABORTED:
+				wrk->stats->sess_fail_econnaborted++;
+				break;
+			case EINTR:
+				wrk->stats->sess_fail_eintr++;
 				break;
 			case EMFILE:
-				VSL(SLT_Debug, ls->sock, "Too many open files");
+				wrk->stats->sess_fail_emfile++;
 				vca_pace_bad();
 				break;
 			case EBADF:
-				VSL(SLT_Debug, ls->sock, "Accept failed: %s",
-				    strerror(errno));
+				wrk->stats->sess_fail_ebadf++;
+				vca_pace_bad();
+				break;
+			case ENOBUFS:
+			case ENOMEM:
+				wrk->stats->sess_fail_enomem++;
 				vca_pace_bad();
 				break;
 			default:
-				VSL(SLT_Debug, ls->sock, "Accept failed: %s",
-				    strerror(errno));
+				wrk->stats->sess_fail_other++;
 				vca_pace_bad();
 				break;
 			}
 			wrk->stats->sess_fail++;
+			VSL(SLT_Debug, ls->sock, "Accept failed: %s",
+			    strerror(errno));
 			(void)Pool_TrySumstat(wrk);
 			continue;
 		}
diff --git a/doc/changes.rst b/doc/changes.rst
index c1e996fa06..97ce46696f 100644
--- a/doc/changes.rst
+++ b/doc/changes.rst
@@ -37,6 +37,20 @@ varnishadm
 * The output format of the ``backend.list`` CLI command has been
   changed.
 
+varnishstat
+-----------
+
+* The counters
+
+  * ``sess_fail_econnaborted``
+  * ``sess_fail_eintr``
+  * ``sess_fail_emfile``
+  * ``sess_fail_ebadf``
+  * ``sess_fail_enomem``
+  * ``sess_fail_other``
+
+  now break down the detailled reason for session accept failures, the
+  sum of which continues to be counted in ``sess_fail``.
 
 VCL and bundled VMODs
 ---------------------