diff --git a/.gitignore b/.gitignore
index 21286094..def5770d 100644
--- a/.gitignore
+++ b/.gitignore
@@ -34,3 +34,4 @@ docs/_build
 /.eggs
 /.vscode
 /.mypy_cache
+.venv
diff --git a/asyncpg/connect_utils.py b/asyncpg/connect_utils.py
index 4d1a3f7d..f36851b3 100644
--- a/asyncpg/connect_utils.py
+++ b/asyncpg/connect_utils.py
@@ -10,6 +10,9 @@
 import enum
 import functools
 import getpass
+import inspect
+import logging
+import random
 import os
 import pathlib
 import platform
@@ -23,12 +26,10 @@
 import typing
 import urllib.parse
 import warnings
-import inspect
 
-from . import compat
-from . import exceptions
-from . import protocol
+from . import compat, exceptions, protocol
 
+logger = logging.getLogger(__name__)
 
 class SSLMode(enum.IntEnum):
     disable = 0
@@ -882,21 +883,24 @@ async def __connect_addr(
     return con
 
 
-async def _connect(*, loop, timeout, connection_class, record_class, **kwargs):
+async def _connect(*, loop, timeout, connection_class, record_class, connect_timeout=60, **kwargs):
     if loop is None:
         loop = asyncio.get_event_loop()
 
-    addrs, params, config = _parse_connect_arguments(timeout=timeout, **kwargs)
+    addrs, params, config = _parse_connect_arguments(timeout=connect_timeout, **kwargs)
 
-    last_error = None
+    random.shuffle(addrs)
+    last_error = ConnectionError(f"Can't connect to all hosts {addrs}")
     addr = None
     for addr in addrs:
+        if timeout <= 0:
+            raise ConnectionError("Timeout")
         before = time.monotonic()
         try:
             return await _connect_addr(
                 addr=addr,
                 loop=loop,
-                timeout=timeout,
+                timeout=connect_timeout,
                 params=params,
                 config=config,
                 connection_class=connection_class,
@@ -904,6 +908,7 @@ async def _connect(*, loop, timeout, connection_class, record_class, **kwargs):
             )
         except (OSError, asyncio.TimeoutError, ConnectionError) as ex:
             last_error = ex
+            logger.warning("Can't connect to %s: %s", addr, ex, exc_info=True)
         finally:
             timeout -= time.monotonic() - before
 
diff --git a/asyncpg/connection.py b/asyncpg/connection.py
index 73cb6e66..91667a28 100644
--- a/asyncpg/connection.py
+++ b/asyncpg/connection.py
@@ -1784,6 +1784,7 @@ async def connect(dsn=None, *,
                   database=None,
                   loop=None,
                   timeout=60,
+                  connect_timeout=60,
                   statement_cache_size=100,
                   max_cached_statement_lifetime=300,
                   max_cacheable_statement_size=1024 * 15,
@@ -2104,6 +2105,7 @@ async def connect(dsn=None, *,
         ssl=ssl,
         direct_tls=direct_tls,
         database=database,
+        connect_timeout=connect_timeout,
         server_settings=server_settings,
         command_timeout=command_timeout,
         statement_cache_size=statement_cache_size,