diff --git a/asyncpg/connect_utils.py b/asyncpg/connect_utils.py
index 8d80dc29..86259be3 100644
--- a/asyncpg/connect_utils.py
+++ b/asyncpg/connect_utils.py
@@ -729,7 +729,7 @@ async def _connect(*, loop, timeout, connection_class, record_class, **kwargs):
     for addr in addrs:
         before = time.monotonic()
         try:
-            con = await _connect_addr(
+            return await _connect_addr(
                 addr=addr,
                 loop=loop,
                 timeout=timeout,
@@ -740,8 +740,6 @@ async def _connect(*, loop, timeout, connection_class, record_class, **kwargs):
             )
         except (OSError, asyncio.TimeoutError, ConnectionError) as ex:
             last_error = ex
-        else:
-            return con
         finally:
             timeout -= time.monotonic() - before
 
diff --git a/asyncpg/connection.py b/asyncpg/connection.py
index 043c6ddd..3f678d16 100644
--- a/asyncpg/connection.py
+++ b/asyncpg/connection.py
@@ -9,11 +9,13 @@
 import asyncpg
 import collections
 import collections.abc
+import functools
 import itertools
 import sys
 import time
 import traceback
 import warnings
+import weakref
 
 from . import compat
 from . import connect_utils
@@ -70,7 +72,8 @@ def __init__(self, protocol, transport, loop,
         self._stmt_cache = _StatementCache(
             loop=loop,
             max_size=config.statement_cache_size,
-            on_remove=self._maybe_gc_stmt,
+            on_remove=functools.partial(
+                _weak_maybe_gc_stmt, weakref.ref(self)),
             max_lifetime=config.max_cached_statement_lifetime)
 
         self._stmts_to_close = set()
@@ -2260,4 +2263,10 @@ def _check_record_class(record_class):
         )
 
 
+def _weak_maybe_gc_stmt(weak_ref, stmt):
+    self = weak_ref()
+    if self is not None:
+        self._maybe_gc_stmt(stmt)
+
+
 _uid = 0
diff --git a/tests/test_connect.py b/tests/test_connect.py
index 7b08f93d..ff884af8 100644
--- a/tests/test_connect.py
+++ b/tests/test_connect.py
@@ -7,7 +7,6 @@
 
 import asyncio
 import contextlib
-import gc
 import ipaddress
 import os
 import platform
@@ -1448,14 +1447,11 @@ class TestConnectionGC(tb.ClusterTestCase):
 
     async def _run_no_explicit_close_test(self):
         con = await self.connect()
+        await con.fetchval("select 123")
         proto = con._protocol
         conref = weakref.ref(con)
         del con
 
-        gc.collect()
-        gc.collect()
-        gc.collect()
-
         self.assertIsNone(conref())
         self.assertTrue(proto.is_closed())