diff --git a/lib/web_push/connections.rb b/lib/web_push/connections.rb
index 24a13aa..be6191a 100644
--- a/lib/web_push/connections.rb
+++ b/lib/web_push/connections.rb
@@ -42,7 +42,7 @@ class WebPush::Connections
 
   def request(http, request)
     unless http.is_a?(HTTP) && http.ipaddr && !http.proxy? && http.use_ssl? && !http.started?
-      raise ArgumentError, "Only new, direct TLS connections pinned to an address are pooled"
+      raise ArgumentError, "Only new, direct TLS connections pinned to an address and opened as WebPush::Connections::HTTP are pooled"
     end
     address = [ http.address, http.port, http.ipaddr ]
 
diff --git a/test/lib/web_push/connections_test.rb b/test/lib/web_push/connections_test.rb
index b93ced3..9eb2b2b 100644
--- a/test/lib/web_push/connections_test.rb
+++ b/test/lib/web_push/connections_test.rb
@@ -97,14 +97,15 @@ class WebPush::ConnectionsTest < ActiveSupport::TestCase
     end
   end
 
-  test "only new, direct TLS connections pinned to an address are pooled" do
+  test "only new, direct TLS connections pinned to an address and opened as WebPush::Connections::HTTP are pooled" do
     with_push_service do |server|
-      unpinned = Net::HTTP.new(HOST, server.port, nil).tap { it.use_ssl = true }
-      proxied = Net::HTTP.new(HOST, server.port, "127.0.0.1", 3128).tap { it.ipaddr = IP; it.use_ssl = true }
+      unpinned = WebPush::Connections::HTTP.new(HOST, server.port, nil).tap { it.use_ssl = true }
+      proxied = WebPush::Connections::HTTP.new(HOST, server.port, "127.0.0.1", 3128).tap { it.ipaddr = IP; it.use_ssl = true }
       plain = pinned_connection(server).tap { it.use_ssl = false }
       started = pinned_connection(server).tap(&:start)
+      untracked = Net::HTTP.new(HOST, server.port, nil).tap { it.ipaddr = IP; it.use_ssl = true }
 
-      [ unpinned, proxied, plain, started ].each do |http|
+      [ unpinned, proxied, plain, started, untracked ].each do |http|
         assert_raises(ArgumentError) { @connections.request(http, push_request) }
       end
       assert_empty server.requests