diff --git a/internal/experiment/webconnectivity/analysiscore.go b/internal/experiment/webconnectivity/analysiscore.go
index e92c908..3723928 100644
--- a/internal/experiment/webconnectivity/analysiscore.go
+++ b/internal/experiment/webconnectivity/analysiscore.go
@@ -1,6 +1,11 @@
 package webconnectivity
 
-import "github.com/ooni/probe-cli/v3/internal/model"
+import (
+	"fmt"
+	"net"
+
+	"github.com/ooni/probe-cli/v3/internal/model"
+)
 
 //
 // Core analysis
@@ -83,6 +88,9 @@ const (
 //     +--------------------------------------+----------------+-------------+
 //
 // It's a very simple rule, that should preserve previous semantics.
+//
+// As an improvement over Web Connectivity v0.4, we also attempt to identify
+// special subcases of a null, null result to provide the user with more information.
 func (tk *TestKeys) analysisToplevel(logger model.Logger) {
 	// Since we run after all tasks have completed (or so we assume) we're
 	// not going to use any form of locking here.
@@ -135,11 +143,20 @@ func (tk *TestKeys) analysisToplevel(logger model.Logger) {
 		)
 
 	default:
-		if tk.analysisNullNullDetectNoAddrs(logger) {
+		if tk.analysisWebsiteDownDetectNoAddrs(logger) {
 			tk.Blocking = false
 			tk.Accessible = false
 			logger.Infof(
-				"NO_AVAILABLE_ADDRS: flags=%d, accessible=%+v, blocking=%+v",
+				"WEBSITE_DOWN_DNS: flags=%d, accessible=%+v, blocking=%+v",
+				tk.BlockingFlags, tk.Accessible, tk.Blocking,
+			)
+			return
+		}
+		if tk.analysisWebsiteDownDetectAllConnectsFailed(logger) {
+			tk.Blocking = false
+			tk.Accessible = false
+			logger.Infof(
+				"WEBSITE_DOWN_TCP: flags=%d, accessible=%+v, blocking=%+v",
 				tk.BlockingFlags, tk.Accessible, tk.Blocking,
 			)
 			return
@@ -154,12 +171,58 @@ func (tk *TestKeys) analysisToplevel(logger model.Logger) {
 }
 
 const (
-	// analysisFlagNullNullNoAddrs indicates neither the probe nor the TH were
+	// analysisFlagWebsiteDownNoAddrs indicates neither the probe nor the TH were
 	// able to get any IP addresses from any resolver.
-	analysisFlagNullNullNoAddrs = 1 << iota
+	analysisFlagWebsiteDownNoAddrs = 1 << iota
+
+	// analysisFlagWebsiteDownAllConnectsFailed indicates that all the connect
+	// attempts failed both in the probe and in the test helper.
+	analysisFlagWebsiteDownAllConnectsFailed
 )
 
-// analysisNullNullDetectNoAddrs attempts to see whether we
+// analysisWebsiteDownDetectAllConnectsFailed attempts to detect whether we are in
+// the .Blocking = nil, .Accessible = nil case because all the TCP connect
+// attempts by either the probe or the TH have failed.
+//
+// See https://explorer.ooni.org/measurement/20220911T105037Z_webconnectivity_IT_30722_n1_ruzuQ219SmIO9SrT?input=https://doh.centraleu.pi-dns.com/dns-query?dns=q80BAAABAAAAAAAAA3d3dwdleGFtcGxlA2NvbQAAAQAB
+// for an example measurement with this behavior.
+//
+// See https://github.com/ooni/probe/issues/2299 for the reference issue.
+func (tk *TestKeys) analysisWebsiteDownDetectAllConnectsFailed(logger model.Logger) bool {
+	if tk.Control == nil {
+		// we need control data to say we're in this case
+		return false
+	}
+
+	for _, entry := range tk.TCPConnect {
+		if entry.Status.Failure == nil {
+			// we need all connect attempts to fail
+			return false
+		}
+		epnt := net.JoinHostPort(entry.IP, fmt.Sprintf("%d", entry.Port))
+		thEntry, found := tk.Control.TCPConnect[epnt]
+		if !found {
+			// we need exactly the same attempts to have failed
+			return false
+		}
+		if thEntry.Failure == nil {
+			// we need all TH attempts to fail
+			return false
+		}
+	}
+
+	// only if we have had some addresses to connect
+	if len(tk.TCPConnect) > 0 && len(tk.Control.TCPConnect) > 0 {
+		logger.Info("website likely down: all TCP connect attempts failed for both probe and TH")
+		tk.WebsiteDownFlags |= analysisFlagWebsiteDownAllConnectsFailed
+		return true
+	}
+
+	// safety net in case we're passed empty lists/maps
+	return false
+}
+
+// analysisWebsiteDownDetectNoAddrs attempts to see whether we
 // ended up into the .Blocking = nil, .Accessible = nil case because
 // the domain is expired and all queries returned no addresses.
 //
@@ -173,7 +236,7 @@ const (
 //
 // See https://github.com/ooni/probe/issues/2029 for more information
 // on Android's getaddrinfo behavior.
-func (tk *TestKeys) analysisNullNullDetectNoAddrs(logger model.Logger) bool {
+func (tk *TestKeys) analysisWebsiteDownDetectNoAddrs(logger model.Logger) bool {
 	if tk.Control == nil {
 		// we need control data to say we're in this case
 		return false
@@ -200,7 +263,7 @@ func (tk *TestKeys) analysisNullNullDetectNoAddrs(logger model.Logger) bool {
 		// when the TH used addresses, we're not in the NoAddresses case
 		return false
 	}
-	logger.Infof("Neither the probe nor the TH resolved any addresses")
-	tk.NullNullFlags |= analysisFlagNullNullNoAddrs
+	logger.Infof("website likely down: all DNS lookups failed for both probe and TH")
+	tk.WebsiteDownFlags |= analysisFlagWebsiteDownNoAddrs
 	return true
 }
diff --git a/internal/experiment/webconnectivity/measurer.go b/internal/experiment/webconnectivity/measurer.go
index 592c8ba..5b01fa8 100644
--- a/internal/experiment/webconnectivity/measurer.go
+++ b/internal/experiment/webconnectivity/measurer.go
@@ -36,7 +36,7 @@ func (m *Measurer) ExperimentName() string {
 
 // ExperimentVersion implements model.ExperimentMeasurer.
 func (m *Measurer) ExperimentVersion() string {
-	return "0.5.11"
+	return "0.5.12"
 }
 
 // Run implements model.ExperimentMeasurer.
diff --git a/internal/experiment/webconnectivity/testkeys.go b/internal/experiment/webconnectivity/testkeys.go
index 327bb7c..e089e3e 100644
--- a/internal/experiment/webconnectivity/testkeys.go
+++ b/internal/experiment/webconnectivity/testkeys.go
@@ -72,7 +72,7 @@ type TestKeys struct {
 	// ControlFailure contains the failure of the control experiment.
 	ControlFailure *string `json:"control_failure"`
 
-	// DNSFlags contains DNS analysis flags.
+	// DNSFlags describes specific DNS anomalies we observed.
 	DNSFlags int64 `json:"x_dns_flags"`
 
 	// DNSExperimentFailure indicates whether there was a failure in any
@@ -87,13 +87,11 @@ type TestKeys struct {
 	// the final HTTP request that we recorded.
 	HTTPExperimentFailure *string `json:"http_experiment_failure"`
 
-	// BlockingFlags contains blocking flags.
+	// BlockingFlags explains why we think that the website is blocked.
 	BlockingFlags int64 `json:"x_blocking_flags"`
 
-	// NullNullFlags explains why we determined that a measurement is not
-	// failed by detecting specific conditions that would have otherwise
-	// caused .Accessible = nil and .Blocking = nil
-	NullNullFlags int64 `json:"x_null_null_flags"`
+	// WebsiteDownFlags explains why we determined that the website is down.
+	WebsiteDownFlags int64 `json:"x_website_down_flags"`
 
 	// BodyLength match tells us whether the body length matches.
 	BodyLengthMatch *bool `json:"body_length_match"`
@@ -339,7 +337,7 @@ func NewTestKeys() *TestKeys {
 		DNSConsistency:        "",
 		HTTPExperimentFailure: nil,
 		BlockingFlags:         0,
-		NullNullFlags:         0,
+		WebsiteDownFlags:      0,
 		BodyLengthMatch:       nil,
 		HeadersMatch:          nil,
 		StatusCodeMatch:       nil,