diff --git a/src/net.rs b/src/net.rs
index dad174a2eb..aeb0b4867d 100644
--- a/src/net.rs
+++ b/src/net.rs
@@ -8,6 +8,7 @@ use async_native_tls::TlsStream;
 use tokio::net::TcpStream;
 use tokio::time::timeout;
 use tokio_io_timeout::TimeoutStream;
+use tokio::task::JoinSet;
 
 use crate::context::Context;
 use crate::sql::Sql;
@@ -151,22 +152,78 @@ pub(crate) async fn connect_tcp(
     port: u16,
     load_cache: bool,
 ) -> Result<Pin<Box<TimeoutStream<TcpStream>>>> {
+    let mut connection_attempt_set = JoinSet::new();
+    let mut delay_set = JoinSet::new();
+
+    let mut connection_futures = Vec::new();
+    for resolved_addr in lookup_host_with_cache(context, host, port, "", load_cache)
+        .await?
+        .into_iter()
+        .rev()
+    {
+        let fut = connect_tcp_inner(resolved_addr);
+        connection_futures.push(fut);
+    }
+
+    // Start with one connection.
+    if let Some(fut) = connection_futures.pop() {
+        connection_attempt_set.spawn(fut);
+    }
+
+    for delay in CONNECTION_DELAYS {
+        delay_set.spawn(tokio::time::sleep(delay));
+    }
+
     let mut first_error = None;
 
-    for resolved_addr in lookup_host_with_cache(context, host, port, "", load_cache).await? {
-        match connect_tcp_inner(resolved_addr).await {
-            Ok(stream) => {
-                return Ok(stream);
-            }
-            Err(err) => {
-                warn!(
-                    context,
-                    "Failed to connect to {}: {:#}.", resolved_addr, err
-                );
-                first_error.get_or_insert(err);
+    loop {
+        tokio::select! {
+            biased;
+
+            res = connection_attempt_set.join_next() => {
+                match res {
+                    Some(res) => {
+                        match res.context("Failed to join task")? {
+                            Ok(conn) => {
+                                // Successfully connected.
+                                return Ok(conn);
+                            },
+                            Err(err) => {
+                                // Some connection attempt failed.
+                                first_error.get_or_insert(err);
+                            }
+                        }
+                    },
+                    None => {
+                        // Out of connection attempts.
+                        //
+                        // Break out of the loop and return error.
+                        break;
+                    }
+                }
+            },
+            _ = delay_set.join_next(), if !delay_set.is_empty() => {
+                // Delay expired.
+                //
+                // Don't do anything other than adding
+                // another connection attempt to the active set.
             }
         }
+
+        if let Some(fut) = connection_futures.pop() {
+            connection_attempt_set.spawn(fut);
+        }
     }
 
+    // Abort remaining connection attempts and free resources
+    // such as OS sockets and `Context` references
+    // held by connection attempt tasks.
+    //
+    // `delay_set` contains just `sleep` tasks
+    // so no need to await futures there,
+    // it is enough that futures are aborted
+    // when the set is dropped.
+    connection_attempt_set.shutdown().await;
+
     Err(first_error.unwrap_or_else(|| format_err!("no DNS resolution results for {host}")))
 }