diff --git a/vertx-pg-client/src/main/java/io/vertx/pgclient/impl/InitiateSslHandler.java b/vertx-pg-client/src/main/java/io/vertx/pgclient/impl/InitiateSslHandler.java
index 402c3d2d8..4d08162d7 100644
--- a/vertx-pg-client/src/main/java/io/vertx/pgclient/impl/InitiateSslHandler.java
+++ b/vertx-pg-client/src/main/java/io/vertx/pgclient/impl/InitiateSslHandler.java
@@ -75,10 +75,13 @@ public void channelRead(ChannelHandlerContext ctx, Object msg) throws Exception
       }
       case PgProtocolConstants.MESSAGE_TYPE_SSL_NO: {
         upgradePromise.fail(new Exception("Postgres Server does not handle SSL connection"));
+        // The server waits for a startup message on this socket: close it, PREFER reconnects without SSL
+        ctx.close();
         break;
       }
       default:
         upgradePromise.fail(new Exception("Invalid SSL connection message"));
+        ctx.close();
         break;
     }
   }
diff --git a/vertx-pg-client/src/test/java/io/vertx/tests/pgclient/TLSTest.java b/vertx-pg-client/src/test/java/io/vertx/tests/pgclient/TLSTest.java
index 9c1178979..59be2d2b3 100644
--- a/vertx-pg-client/src/test/java/io/vertx/tests/pgclient/TLSTest.java
+++ b/vertx-pg-client/src/test/java/io/vertx/tests/pgclient/TLSTest.java
@@ -24,9 +24,12 @@
 import io.vertx.pgclient.*;
 import io.vertx.sqlclient.Tuple;
 import io.vertx.tests.pgclient.junit.ContainerPgRule;
+import io.vertx.tests.sqlclient.ProxyServer;
 import org.junit.*;
 import org.junit.runner.RunWith;
 
+import java.util.concurrent.atomic.AtomicInteger;
+
 @RunWith(VertxUnitRunner.class)
 public class TLSTest {
 
@@ -150,6 +153,32 @@ public void testSslModePreferFallback(TestContext ctx) {
     }));
   }
 
+  @Test
+  public void testSslModeRequireClosesRefusedSocket(TestContext ctx) {
+    PgConnectOptions options = ruleSllOff.options()
+      .setSslMode(SslMode.REQUIRE)
+      .setSslOptions(new ClientSSLOptions().setTrustAll(true));
+    AtomicInteger openSockets = new AtomicInteger();
+    ProxyServer proxy = ProxyServer.create(vertx, options.getPort(), options.getHost());
+    proxy.proxyHandler(conn -> {
+      openSockets.incrementAndGet();
+      conn.clientCloseHandler(v -> openSockets.decrementAndGet());
+      conn.connect();
+    });
+    Async listen = ctx.async();
+    proxy.listen(8080, "localhost", ctx.asyncAssertSuccess(v -> listen.complete()));
+    listen.awaitSuccess(10000);
+    options.setPort(8080).setHost("localhost");
+    Async async = ctx.async();
+    PgConnection.connect(vertx, options).onComplete(ctx.asyncAssertFailure(err -> {
+      // The server refused SSL: the client must not keep the socket it opened to ask for it
+      vertx.setTimer(2000, id -> {
+        ctx.assertEquals(0, openSockets.get());
+        async.complete();
+      });
+    }));
+  }
+
   @Test
   public void testSslModeVerifyCaConf(TestContext ctx) {
     PgConnectOptions options = ruleOptionalSll.options()