diff --git a/src/main/java/io/vertx/core/http/HttpConnection.java b/src/main/java/io/vertx/core/http/HttpConnection.java
index c3fbf548b29..63643a6d691 100644
--- a/src/main/java/io/vertx/core/http/HttpConnection.java
+++ b/src/main/java/io/vertx/core/http/HttpConnection.java
@@ -23,6 +23,7 @@
 import javax.security.cert.X509Certificate;
 import java.security.cert.Certificate;
 import java.util.List;
+import java.util.concurrent.TimeUnit;
 
 /**
  * Represents an HTTP connection.
@@ -119,38 +120,64 @@ default HttpConnection goAway(long errorCode, int lastStreamId) {
   HttpConnection shutdownHandler(@Nullable  Handler<Void> handler);
 
   /**
-   * Initiate a graceful connection shutdown, the connection is taken out of service and closed when all current requests
-   * are processed, otherwise after 30 seconds the connection will be closed. Client connection are immediately removed
-   * from the pool.
-   *
-   * <ul>
-   *   <li>HTTP/2 connections will send a go away frame immediately to signal the other side the connection will close</li>
-   *   <li>HTTP/1.x client connection supports this feature</li>
-   *   <li>HTTP/1.x server connections do not support this feature</li>
-   * </ul>
-   *
-   * @param handler the handler called when shutdown has completed
+   * Shutdown a 30 seconds timeout ({@code shutdown(30, TimeUnit.SECONDS)}).
    */
   default void shutdown(Handler<AsyncResult<Void>> handler) {
-    shutdown(30000, handler);
+    shutdown(30, TimeUnit.SECONDS, handler);
   }
 
   /**
    * Like {@link #shutdown(Handler)} but returns a {@code Future} of the asynchronous result
    */
   default Future<Void> shutdown() {
-    return shutdown(30000L);
+    return shutdown(30, TimeUnit.SECONDS);
   }
 
   /**
-   * Like {@link #shutdown(Handler)} but with a specific {@code timeout} in milliseconds.
+   * Like {@link #shutdown(long, TimeUnit, Handler)}, in milliseconds.
+   *
+   * @deprecated instead use {@link #shutdown(long, TimeUnit, Handler)}
    */
-  void shutdown(long timeout, Handler<AsyncResult<Void>> handler);
+  @Deprecated
+  default void shutdown(long timeout, Handler<AsyncResult<Void>> handler) {
+    shutdown(timeout, TimeUnit.MILLISECONDS, handler);
+  }
 
   /**
    * Like {@link #shutdown(long, Handler)} but returns a {@code Future} of the asynchronous result
+   *
+   * @deprecated instead use {@link #shutdown(long, TimeUnit)}
+   */
+  @Deprecated
+  default Future<Void> shutdown(long timeoutMs) {
+    return shutdown(timeoutMs, TimeUnit.MILLISECONDS);
+  }
+
+  /**
+   * Initiate a graceful connection shutdown, the connection is taken out of service and closed when all the inflight requests
+   * are processed, otherwise after a {@code timeout} the connection will be closed. Client connection are immediately removed
+   * from the pool.
+   *
+   * <ul>
+   *   <li>HTTP/2 connections will send a go away frame immediately to signal the other side the connection will close.</li>
+   *   <li>HTTP/1.x connection will be closed.</li>
+   * </ul>
+   *
+   * @param timeout the amount of time after which all resources are forcibly closed
+   * @param unit the of the timeout
+   * @param handler the handler notified with the result
+   */
+  default void shutdown(long timeout, TimeUnit unit, Handler<AsyncResult<Void>> handler) {
+    Future<Void> fut = shutdown(timeout, unit);
+    if (handler != null) {
+      fut.onComplete(handler);
+    }
+  }
+
+  /**
+   * Like {@link #shutdown(long, TimeUnit, Handler)} but returns a {@code Future} of the asynchronous result
    */
-  Future<Void> shutdown(long timeoutMs);
+  Future<Void> shutdown(long timeout, TimeUnit unit);
 
   /**
    * Set a close handler. The handler will get notified when the connection is closed.
diff --git a/src/main/java/io/vertx/core/http/impl/Http1xClientConnection.java b/src/main/java/io/vertx/core/http/impl/Http1xClientConnection.java
index 5421b0459eb..021ab548b26 100644
--- a/src/main/java/io/vertx/core/http/impl/Http1xClientConnection.java
+++ b/src/main/java/io/vertx/core/http/impl/Http1xClientConnection.java
@@ -56,6 +56,7 @@
 
 import java.net.URI;
 import java.util.*;
+import java.util.concurrent.TimeUnit;
 import java.util.function.BiConsumer;
 
 import static io.netty.handler.codec.http.websocketx.WebSocketVersion.*;
@@ -1284,23 +1285,18 @@ public boolean isValid() {
     return expirationTimestamp == 0 || System.currentTimeMillis() <= expirationTimestamp;
   }
 
-  @Override
-  public void shutdown(long timeout, Handler<AsyncResult<Void>> handler) {
-    shutdown(timeout, vertx.promise(handler));
+  private synchronized void shutdownNow() {
+    shutdownTimerID = -1L;
+    close();
   }
 
   @Override
-  public Future<Void> shutdown(long timeoutMs) {
+  public Future<Void> shutdown(long timeout, TimeUnit unit) {
     PromiseInternal<Void> promise = vertx.promise();
-    shutdown(timeoutMs, promise);
+    shutdown(unit.toMillis(timeout), promise);
     return promise.future();
   }
 
-  private synchronized void shutdownNow() {
-    shutdownTimerID = -1L;
-    close();
-  }
-
   private void shutdown(long timeoutMs, PromiseInternal<Void> promise) {
     synchronized (this) {
       if (shutdown) {
diff --git a/src/main/java/io/vertx/core/http/impl/Http1xConnectionBase.java b/src/main/java/io/vertx/core/http/impl/Http1xConnectionBase.java
index de41192dc72..53aed89ec09 100644
--- a/src/main/java/io/vertx/core/http/impl/Http1xConnectionBase.java
+++ b/src/main/java/io/vertx/core/http/impl/Http1xConnectionBase.java
@@ -41,6 +41,8 @@
 import io.vertx.core.impl.ContextInternal;
 import io.vertx.core.net.impl.ConnectionBase;
 
+import java.util.concurrent.TimeUnit;
+
 import static io.vertx.core.net.impl.VertxHandler.safeBuffer;
 
 /**
@@ -132,12 +134,7 @@ public HttpConnection shutdownHandler(@Nullable Handler<Void> handler) {
   }
 
   @Override
-  public void shutdown(long timeout, Handler<AsyncResult<Void>> handler) {
-    throw new UnsupportedOperationException("HTTP/1.x connections cannot be shutdown");
-  }
-
-  @Override
-  public Future<Void> shutdown(long timeoutMs) {
+  public Future<Void> shutdown(long timeout, TimeUnit unit) {
     throw new UnsupportedOperationException("HTTP/1.x connections cannot be shutdown");
   }
 
diff --git a/src/main/java/io/vertx/core/http/impl/Http2ConnectionBase.java b/src/main/java/io/vertx/core/http/impl/Http2ConnectionBase.java
index 7a31c834c33..e72fa16ede5 100644
--- a/src/main/java/io/vertx/core/http/impl/Http2ConnectionBase.java
+++ b/src/main/java/io/vertx/core/http/impl/Http2ConnectionBase.java
@@ -47,6 +47,7 @@
 import java.util.ArrayList;
 import java.util.Map;
 import java.util.Objects;
+import java.util.concurrent.TimeUnit;
 
 /**
  * @author <a href="mailto:julien@julienviet.com">Julien Viet</a>
@@ -363,14 +364,9 @@ public synchronized HttpConnection shutdownHandler(Handler<Void> handler) {
   }
 
   @Override
-  public void shutdown(long timeout, Handler<AsyncResult<Void>> handler) {
-    shutdown(timeout, vertx.promise(handler));
-  }
-
-  @Override
-  public Future<Void> shutdown(long timeoutMs) {
+  public Future<Void> shutdown(long timeout, TimeUnit unit) {
     PromiseInternal<Void> promise = vertx.promise();
-    shutdown(timeoutMs, promise);
+    shutdown(unit.toMillis(timeout), promise);
     return promise.future();
   }
 
diff --git a/src/main/java/io/vertx/core/http/impl/Http2UpgradeClientConnection.java b/src/main/java/io/vertx/core/http/impl/Http2UpgradeClientConnection.java
index e61ed9158e1..f8ca98e5776 100644
--- a/src/main/java/io/vertx/core/http/impl/Http2UpgradeClientConnection.java
+++ b/src/main/java/io/vertx/core/http/impl/Http2UpgradeClientConnection.java
@@ -38,6 +38,7 @@
 import java.util.ArrayDeque;
 import java.util.Deque;
 import java.util.List;
+import java.util.concurrent.TimeUnit;
 
 /**
  * A connection that attempts to perform a protocol upgrade to H2C. The connection might use HTTP/1 or H2C
@@ -885,13 +886,8 @@ public HttpConnection goAway(long errorCode, int lastStreamId, Buffer debugData)
   }
 
   @Override
-  public void shutdown(long timeout, Handler<AsyncResult<Void>> handler) {
-    current.shutdown(timeout, handler);
-  }
-
-  @Override
-  public Future<Void> shutdown(long timeoutMs) {
-    return current.shutdown(timeoutMs);
+  public Future<Void> shutdown(long timeout, TimeUnit unit) {
+    return current.shutdown(timeout, unit);
   }
 
   @Override