diff --git a/Lib/subprocess.py b/Lib/subprocess.py
index 88355ada1b4..0942d94ef71 100644
--- a/Lib/subprocess.py
+++ b/Lib/subprocess.py
@@ -1341,6 +1341,13 @@ class Popen(object):
             # Data format: "exception name:hex errno:description"
             # Pickle is not used; it is complex and involves memory allocation.
             errpipe_read, errpipe_write = os.pipe()
+            # errpipe_write must not be in the standard io 0, 1, or 2 fd range.
+            low_fds_to_close = []
+            while errpipe_write < 3:
+                low_fds_to_close.append(errpipe_write)
+                errpipe_write = os.dup(errpipe_write)
+            for low_fd in low_fds_to_close:
+                os.close(low_fd)
             try:
                 try:
                     # We must avoid complex work that could involve
diff --git a/Lib/test/test_subprocess.py b/Lib/test/test_subprocess.py
index 54f648265f6..46e012d142c 100644
--- a/Lib/test/test_subprocess.py
+++ b/Lib/test/test_subprocess.py
@@ -1559,6 +1559,27 @@ class POSIXProcessTestCase(BaseTestCase):
         # all standard fds closed.
         self.check_close_std_fds([0, 1, 2])
 
+    def test_small_errpipe_write_fd(self):
+        """Issue #15798: Popen should work when stdio fds are available."""
+        new_stdin = os.dup(0)
+        new_stdout = os.dup(1)
+        try:
+            os.close(0)
+            os.close(1)
+
+            # Side test: if errpipe_write fails to have its CLOEXEC
+            # flag set this should cause the parent to think the exec
+            # failed.  Extremely unlikely: everyone supports CLOEXEC.
+            subprocess.Popen([
+                    sys.executable, "-c",
+                    "print('AssertionError:0:CLOEXEC failure.')"]).wait()
+        finally:
+            # Restore original stdin and 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)]
diff --git a/Misc/NEWS b/Misc/NEWS
index 4a837d476b3..47579cbba3a 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -18,6 +18,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #15798: Fixed subprocess.Popen() to no longer fail if file
+  descriptor 0, 1 or 2 is closed.
+
 - Issue #17897: Optimized unpickle prefetching.
 
 - Issue #3693: Make the error message more helpful when the array.array()