diff --git a/hscontrol/mapper/mapper.go b/hscontrol/mapper/mapper.go
index 9053f3459..a6704f366 100644
--- a/hscontrol/mapper/mapper.go
+++ b/hscontrol/mapper/mapper.go
@@ -135,6 +135,16 @@ func generateDNSConfig(
 		dnsConfig.CertDomains = []string{domain}
 	}
 
+	// An exit node refuses to proxy these names. Without this, where its OS
+	// resolver reaches MagicDNS, a client allowed only to use the exit node can
+	// read its view of the tailnet through it. Two gaps are deliberate. Without
+	// MagicDNS, base_domain can be a public domain whose names clients ask the
+	// exit node for, so node names stay readable. Reverse lookups stay open, as
+	// on Tailscale SaaS.
+	if dnsConfig.Proxied && cfg.BaseDomain != "" {
+		dnsConfig.ExitNodeFilteredSet = []string{"." + strings.ToLower(cfg.BaseDomain)}
+	}
+
 	return dnsConfig
 }
 
diff --git a/hscontrol/mapper/mapper_test.go b/hscontrol/mapper/mapper_test.go
index 0c37ba133..d0edcdf4a 100644
--- a/hscontrol/mapper/mapper_test.go
+++ b/hscontrol/mapper/mapper_test.go
@@ -42,6 +42,34 @@ var iap = func(ipStr string) *netip.Addr {
 	return &ip
 }
 
+func TestExitNodeFilteredSet(t *testing.T) {
+	tests := []struct {
+		name       string
+		magicDNS   bool
+		baseDomain string
+		want       []string
+	}{
+		{name: "magicdns", magicDNS: true, baseDomain: "Tail.Example.com", want: []string{".tail.example.com"}},
+		{name: "no magicdns", magicDNS: false, baseDomain: "tail.example.com"},
+		{name: "no base domain", magicDNS: true},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := generateDNSConfig(
+				&types.Config{
+					BaseDomain:       tt.baseDomain,
+					TailcfgDNSConfig: &tailcfg.DNSConfig{Proxied: tt.magicDNS},
+				},
+				(&types.Node{}).View(),
+				nil,
+			)
+
+			assert.Equal(t, tt.want, got.ExitNodeFilteredSet)
+		})
+	}
+}
+
 func TestDNSConfigMapResponse(t *testing.T) {
 	tests := []struct {
 		magicDNS bool
diff --git a/hscontrol/servertest/via_compat_test.go b/hscontrol/servertest/via_compat_test.go
index 3baba61cd..ae9264916 100644
--- a/hscontrol/servertest/via_compat_test.go
+++ b/hscontrol/servertest/via_compat_test.go
@@ -144,8 +144,6 @@ var aclMapCompatTests = []string{
 var viaCompatSkipReasons = map[string]string{
 	"tagged-self": "TAGGED_SELF_PROFILE: SaaS gives a tagged node a profile of its own, headscale the shared tagged-devices one",
 
-	"exit-node-filtered-set": "EXIT_NODE_FILTER_UNSET: headscale sends no ExitNodeFilteredSet, so an exit node proxies queries for the tailnet's own names; SaaS sends the suffixes those names sit under",
-
 	"routes-m1-wildcard-src-multi-range/m-odin1/peers":     sameUserPeers,
 	"routes-m1-wildcard-src-multi-range/m-odin2/peers":     sameUserPeers,
 	"routes-m2-member-partial-subnet/m-odin1/peers":        sameUserPeers,