diff --git a/Lib/test/support.py b/Lib/test/support.py
--- a/Lib/test/support.py
+++ b/Lib/test/support.py
@@ -575,10 +575,27 @@ def _is_ipv6_enabled():
 IPV6_ENABLED = _is_ipv6_enabled()
 
 
-# A constant likely larger than the underlying OS pipe buffer size.
+# A constant likely larger than the underlying OS pipe buffer size, to
+# make writes blocking.
 # Windows limit seems to be around 512B, and many Unix kernels have a 64K pipe
-# buffer size or 16*PAGE_SIZE: take a few megs to be sure.  This
+# buffer size or 16*PAGE_SIZE: take a few megs to be sure.
 PIPE_MAX_SIZE = 3 * 1000 * 1000
+if sys.platform == 'linux':
+    # Under Linux 2.6.35 and higher, read the actual buffer size using
+    # F_GETPIPE_SZ (see issue #17835).
+    try:
+        import fcntl
+    except ImportError:
+        pass
+    else:
+        r, w = os.pipe()
+        try:
+            PIPE_MAX_SIZE = fcntl.fcntl(w, 1032) + 1
+        except OSError:
+            pass
+        finally:
+            os.close(r)
+            os.close(w)
 
 
 # decorator for skipping tests on non-IEEE 754 platforms
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -3069,7 +3069,7 @@ class SignalsTest(unittest.TestCase):
             # The buffered IO layer must check for pending signal
             # handlers, which in this case will invoke alarm_interrupt().
             self.assertRaises(ZeroDivisionError,
-                        wio.write, item * (support.PIPE_MAX_SIZE // len(item)))
+                        wio.write, item * (support.PIPE_MAX_SIZE // len(item) + 1))
             t.join()
             # We got one byte, get another one and check that it isn't a
             # repeat of the first one.
@@ -3168,7 +3168,7 @@ class SignalsTest(unittest.TestCase):
         select = support.import_module("select")
         # A quantity that exceeds the buffer size of an anonymous pipe's
         # write end.
-        N = 1024 * 1024
+        N = support.PIPE_MAX_SIZE
         r, w = os.pipe()
         fdopen_kwargs["closefd"] = False
         # We need a separate thread to read from the pipe and allow the