diff --git a/data/hooks/diagnosis/14-ports.py b/data/hooks/diagnosis/14-ports.py
index 05c28e8dc..809407be3 100644
--- a/data/hooks/diagnosis/14-ports.py
+++ b/data/hooks/diagnosis/14-ports.py
@@ -10,10 +10,12 @@ class PortsDiagnoser(Diagnoser):
 
     id_ = os.path.splitext(os.path.basename(__file__))[0].split("-")[1]
     cache_duration = 3600
-    dependencies = ["ip"]
+    dependencies = ["ip", "dnsrecords"]
 
     def run(self):
 
+        # TODO: report a warning if port 53 or 5353 is exposed to the outside world...
+
         # This dict is something like :
         #   {   80: "nginx",
         #       25: "postfix",
@@ -25,28 +27,81 @@ class PortsDiagnoser(Diagnoser):
             for port in infos.get("needs_exposed_ports", []):
                 ports[port] = service
 
-        try:
-            r = Diagnoser.remote_diagnosis('check-ports',
-                                           data={'ports': ports.keys()},
-                                           ipversion=4)
-            results = r["ports"]
-        except Exception as e:
-            raise YunohostError("diagnosis_ports_could_not_diagnose", error=e)
+        ipversions = []
+        ipv4 = Diagnoser.get_cached_report("ip", item={"test": "ipv4"}) or {}
+        if ipv4.get("status") == "SUCCESS":
+            ipversions.append(4)
+
+        # To be discussed: we could also make this check dependent on the
+        # existence of an AAAA record...
+        ipv6 = Diagnoser.get_cached_report("ip", item={"test": "ipv6"}) or {}
+        if ipv6.get("status") == "SUCCESS":
+            ipversions.append(6)
+
+        # Fetch test result for each relevant IP version
+        results = {}
+        for ipversion in ipversions:
+            try:
+                r = Diagnoser.remote_diagnosis('check-ports',
+                                               data={'ports': ports.keys()},
+                                               ipversion=ipversion)
+                results[ipversion] = r["ports"]
+            except Exception as e:
+                raise YunohostError("diagnosis_http_could_not_diagnose", error=e)
+
 
         for port, service in sorted(ports.items()):
+            port = str(port)
             category = services[service].get("category", "[?]")
-            if results.get(str(port), None) is not True:
-                yield dict(meta={"port": str(port)},
-                           data={"service": service, "category": category},
-                           status="ERROR",
-                           summary="diagnosis_ports_unreachable",
-                           details=["diagnosis_ports_needed_by", "diagnosis_ports_forwarding_tip"])
-            else:
-                yield dict(meta={"port": str(port)},
+
+            # If both IPv4 and IPv6 (if applicable) are good
+            if all(results[ipversion].get(port) is True for ipversion in ipversions):
+                yield dict(meta={"port": port},
                            data={"service": service, "category": category},
                            status="SUCCESS",
                            summary="diagnosis_ports_ok",
                            details=["diagnosis_ports_needed_by"])
+            # If both IPv4 and IPv6 (if applicable) are failed
+            elif all(results[ipversion].get(port) is not True for ipversion in ipversions):
+                yield dict(meta={"port": port},
+                           data={"service": service, "category": category},
+                           status="ERROR",
+                           summary="diagnosis_ports_unreachable",
+                           details=["diagnosis_ports_needed_by", "diagnosis_ports_forwarding_tip"])
+            # If only IPv4 is failed or only IPv6 is failed (if applicable)
+            else:
+                passed, failed = (4, 6) if results[4].get(port) is True else (6, 4)
+
+                # Failing in ipv4 is critical.
+                # If we failed in IPv6 but there's in fact no AAAA record
+                # It's an acceptable situation and we shall not report an
+                # error
+                # If any AAAA record is set, IPv6 is important...
+                def ipv6_is_important():
+                    dnsrecords = Diagnoser.get_cached_report("dnsrecords") or {}
+                    return any(record["data"]["AAAA:@"] in ["OK", "WRONG"] for record in dnsrecords.get("items", []))
+
+                if failed == 4 or ipv6_is_important():
+                    yield dict(meta={"port": port},
+                               data={"service": service, "category": category, "passed": passed, "failed": failed},
+                               status="ERROR",
+                               summary="diagnosis_ports_partially_unreachable",
+                               details=["diagnosis_ports_needed_by", "diagnosis_ports_forwarding_tip"])
+                # So otherwise we report a success
+                # And in addition we report an info about the failure in IPv6
+                # *with a different meta* (important to avoid conflicts when
+                # fetching the other info...)
+                else:
+                    yield dict(meta={"port": port},
+                               data={"service": service, "category": category},
+                               status="SUCCESS",
+                               summary="diagnosis_ports_ok",
+                               details=["diagnosis_ports_needed_by"])
+                    yield dict(meta={"test": "ipv6", "port": port},
+                               data={"service": service, "category": category, "passed": passed, "failed": failed},
+                               status="INFO",
+                               summary="diagnosis_ports_partially_unreachable",
+                               details=["diagnosis_ports_needed_by", "diagnosis_ports_forwarding_tip"])
 
 
 def main(args, env, loggers):