diff --git a/Lib/subprocess.py b/Lib/subprocess.py
--- a/Lib/subprocess.py
+++ b/Lib/subprocess.py
@@ -1164,6 +1164,17 @@
             # Data format: "exception name:hex errno:description"
             # Pickle is not used; it is complex and involves memory allocation.
             errpipe_read, errpipe_write = _create_pipe()
+            # Issue 15798: Ensure that errpipe_read & errpipe_write >= 3 so that
+            # they are not clobbered by dup2() calls in child_exec.
+            old_fds = []
+            while errpipe_read < 3:
+                old_fds.append(errpipe_read)
+                errpipe_read = os.dup(errpipe_read)
+            while errpipe_write < 3:
+                old_fds.append(errpipe_write)
+                errpipe_write = os.dup(errpipe_write)
+            for fd in old_fds:
+                os.close(fd)
             try:
                 try:
 
diff --git a/Lib/test/test_subprocess.py b/Lib/test/test_subprocess.py
--- a/Lib/test/test_subprocess.py
+++ b/Lib/test/test_subprocess.py
@@ -1059,6 +1059,23 @@
         # all standard fds closed.
         self.check_close_std_fds([0, 1, 2])
 
+    def test_small_errpipe_write(self):
+        # Issue #15798: test that subprocess pipes still work properly with
+        # fd 0 and 1 closed such that errpipe_read & errpipe_write < 3.
+        # Save stdin & stdout
+        new_stdin = os.dup(0)
+        new_stdout = os.dup(1)
+        os.close(0)
+        os.close(1)
+
+        subprocess.Popen([sys.executable, "-c", 'pass']).wait()
+
+        # Restore old stdin & stdout
+        os.dup2(new_stdin, 0)
+        os.dup2(new_stdout, 1)
+        os.close(new_stdin)
+        os.close(new_stdout)
+
     def test_remapping_std_fds(self):
         # open up some temporary files
         temps = [mkstemp() for i in range(3)]