diff --git a/lib/galaxy/jobs/runners/local.py b/lib/galaxy/jobs/runners/local.py
index 1730ecd4e80..4903dcad37a 100644
--- a/lib/galaxy/jobs/runners/local.py
+++ b/lib/galaxy/jobs/runners/local.py
@@ -5,6 +5,7 @@ import datetime
 import errno
 import logging
 import os
+import signal
 import subprocess
 import tempfile
 import threading
@@ -92,6 +93,10 @@ class LocalJobRunner(BaseJobRunner):
             stdout_file = tempfile.NamedTemporaryFile(mode='wb+', suffix='_stdout', dir=job_wrapper.working_directory)
             stderr_file = tempfile.NamedTemporaryFile(mode='wb+', suffix='_stderr', dir=job_wrapper.working_directory)
             log.debug('(%s) executing job script: %s' % (job_id, command_line))
+            # The preexec_fn argument of Popen() is used to call os.setpgrp() in
+            # the child process just before the child is executed. This will set
+            # the PGID of the child process to its PID (i.e. ensures that it is
+            # the root of its own process group instead of Galaxy's one).
             proc = subprocess.Popen(args=command_line,
                                     shell=True,
                                     cwd=job_wrapper.working_directory,
@@ -161,7 +166,7 @@ class LocalJobRunner(BaseJobRunner):
         if not self._check_pid(pid):
             log.warning("stop_job(): %s: PID %d was already dead or can't be signaled" % (job.id, pid))
             return
-        for sig in [15, 9]:
+        for sig in [signal.SIGTERM, signal.SIGKILL]:
             try:
                 os.killpg(pid, sig)
             except OSError as e:
@@ -216,10 +221,10 @@ class LocalJobRunner(BaseJobRunner):
             return False
 
     def _terminate(self, proc):
-        os.killpg(proc.pid, 15)
+        os.killpg(proc.pid, signal.SIGTERM)
         sleep(1)
         if proc.poll() is None:
-            os.killpg(proc.pid, 9)
+            os.killpg(proc.pid, signal.SIGKILL)
         return proc.wait()  # reap
 
     def _handle_container(self, job_wrapper, proc):
diff --git a/lib/galaxy/jobs/runners/util/__init__.py b/lib/galaxy/jobs/runners/util/__init__.py
index 6f204e8d814..47b67683abe 100644
--- a/lib/galaxy/jobs/runners/util/__init__.py
+++ b/lib/galaxy/jobs/runners/util/__init__.py
@@ -3,7 +3,8 @@ This module and its submodules contains utilities for running external
 processes and interfacing with job managers. This module should contain
 functionality shared between Galaxy and the Pulsar.
 """
-from galaxy.util.bunch import Bunch
 from .kill import kill_pid
 
-__all__ = ('kill_pid', 'Bunch')
+__all__ = (
+    'kill_pid',
+)
diff --git a/lib/galaxy/jobs/runners/util/cli/shell/local.py b/lib/galaxy/jobs/runners/util/cli/shell/local.py
index 2e2f86c17f5..5ab215b9be6 100644
--- a/lib/galaxy/jobs/runners/util/cli/shell/local.py
+++ b/lib/galaxy/jobs/runners/util/cli/shell/local.py
@@ -8,11 +8,9 @@ from time import sleep
 
 import six
 
-from ..shell import BaseShellExec
-from ....util import (
-    Bunch,
-    kill_pid
-)
+from galaxy.util.bunch import Bunch
+from . import BaseShellExec
+from ....util import kill_pid
 
 log = getLogger(__name__)
 
diff --git a/lib/galaxy/jobs/runners/util/kill.py b/lib/galaxy/jobs/runners/util/kill.py
index a95d7e0b51c..6b4e3f8854d 100644
--- a/lib/galaxy/jobs/runners/util/kill.py
+++ b/lib/galaxy/jobs/runners/util/kill.py
@@ -1,4 +1,5 @@
 import os
+import signal
 import subprocess
 from platform import system
 from time import sleep
@@ -55,7 +56,7 @@ def __kill_posix(pid):
             return False
 
     if __check_pid():
-        for sig in [15, 9]:
+        for sig in [signal.SIGTERM, signal.SIGKILL]:
             try:
                 os.killpg(pid, sig)
             except OSError: