diff --git a/src/xopen/__init__.py b/src/xopen/__init__.py
index 9cc7c69..89f5137 100644
--- a/src/xopen/__init__.py
+++ b/src/xopen/__init__.py
@@ -267,6 +267,7 @@ def _open_process(self):
             # data continuously to the process stdin on another thread.
             self.in_thread = threading.Thread(target=self._feed_pipe)
             self.in_thread.start()
+            self._process_explicitly_terminated = False
             self._file: BinaryIO = self.process.stdout  # type: ignore
             self._wait_for_output_or_process_exit()
             self._raise_if_error()
@@ -290,7 +291,11 @@ def _feed_pipe(self):
                 if chunk == b"":
                     self.in_pipe.close()
                     return
-                self.in_pipe.write(chunk)
+                try:
+                    self.in_pipe.write(chunk)
+                except BrokenPipeError:
+                    if not self._process_explicitly_terminated:
+                        raise
         finally:
             self.in_pipe.close()
 
@@ -329,14 +334,15 @@ def close(self) -> None:
             return
         check_allowed_code_and_message = False
         if "r" in self._mode:
-            self._feeding = False
-            self._file.read()
             retcode = self.process.poll()
             if retcode is None:
                 # still running
+                self._process_explicitly_terminated = True
                 self.process.terminate()
                 check_allowed_code_and_message = True
                 self.process.wait()
+            self._feeding = False
+            self._file.read()
             if self.in_thread:
                 self.in_thread.join()
             self._file.close()
diff --git a/tests/conftest.py b/tests/conftest.py
index 33ad423..2a63905 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -10,10 +10,12 @@
 def create_large_file(tmp_path):
     def _create_large_file(extension):
         path = tmp_path / f"large{extension}"
-        random_text = "".join(random.choices(string.ascii_lowercase, k=1024))
-        # Make the text a lot bigger in order to ensure that it is larger than the
-        # pipe buffer size.
-        random_text *= 2048
+        random.seed(0)
+        chars = string.ascii_lowercase + "\n"
+        # Do not decrease this length. The generated file needs to have
+        # a certain length after compression to trigger some bugs
+        # (in particular, 512 kB is not sufficient).
+        random_text = "".join(random.choices(chars, k=1024 * 1024))
         with xopen(path, "w") as f:
             f.write(random_text)
         return path
diff --git a/tests/test_piped.py b/tests/test_piped.py
index ebd5aa3..9f8afbe 100644
--- a/tests/test_piped.py
+++ b/tests/test_piped.py
@@ -6,7 +6,6 @@
 import os
 import shutil
 import sys
-import time
 import pytest
 from pathlib import Path
 from itertools import cycle
@@ -189,8 +188,6 @@ def test_reader_close(reader, create_large_file):
         large_file, "rb", program_settings=program_settings
     ) as f:
         f.readline()
-        time.sleep(0.2)
-    # The subprocess should be properly terminated now
 
 
 def test_invalid_gzip_compression_level(gzip_writer, tmp_path):