diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 6e72180..aef9b1a 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -688,11 +688,12 @@
                 c.settimeout(1.5)
             with self.assertRaises(ZeroDivisionError):
                 signal.alarm(1)
-                c.sendall(b"x" * (1024**2))
+                c.sendall(b"x" * test_support.SOCK_MAX_SIZE)
             if with_timeout:
                 signal.signal(signal.SIGALRM, ok_handler)
                 signal.alarm(1)
-                self.assertRaises(socket.timeout, c.sendall, b"x" * (1024**2))
+                self.assertRaises(socket.timeout, c.sendall,
+                                  b"x" * test_support.SOCK_MAX_SIZE)
         finally:
             signal.signal(signal.SIGALRM, old_alarm)
             c.close()
diff --git a/Lib/test/test_support.py b/Lib/test/test_support.py
index be867bd..1f3c039 100644
--- a/Lib/test/test_support.py
+++ b/Lib/test/test_support.py
@@ -411,8 +411,14 @@
 # Windows limit seems to be around 512 B, and many Unix kernels have a
 # 64 KiB pipe buffer size or 16 * PAGE_SIZE: take a few megs to be sure.
 # (see issue #17835 for a discussion of this number).
-PIPE_MAX_SIZE = 4 *1024 * 1024 + 1
+PIPE_MAX_SIZE = 4 * 1024 * 1024 + 1
 
+# A constant likely larger than the underlying OS socket buffer size, to make
+# writes blocking.
+# The socket buffer sizes can usually be tuned system-wide (e.g. through sysctl
+# on Linux), or on a per-socket basis (SO_SNDBUF/SO_RCVBUF). See issue #18643
+# for a discussion of this number).
+SOCK_MAX_SIZE = 16 * 1024 * 1024 + 1
 
 try:
     unicode