diff --git a/src/DIRAC/WorkloadManagementSystem/Agent/JobAgent.py b/src/DIRAC/WorkloadManagementSystem/Agent/JobAgent.py
index b1d4d05d7c1..15caddd74a8 100755
--- a/src/DIRAC/WorkloadManagementSystem/Agent/JobAgent.py
+++ b/src/DIRAC/WorkloadManagementSystem/Agent/JobAgent.py
@@ -1,9 +1,10 @@
 """
-  The Job Agent class instantiates a CE that acts as a client to a
-  compute resource and also to the WMS.
-  The Job Agent constructs a classAd based on the local resource description in the CS
-  and the current resource status that is used for matching.
+The Job Agent class instantiates a CE that acts as a client to a
+compute resource and also to the WMS.
+The Job Agent constructs a classAd based on the local resource description in the CS
+and the current resource status that is used for matching.
 """
+
 import os
 import re
 import sys
@@ -34,6 +35,7 @@
 from DIRAC.WorkloadManagementSystem.Client.JobReport import JobReport
 from DIRAC.WorkloadManagementSystem.Client.MatcherClient import MatcherClient
 from DIRAC.WorkloadManagementSystem.Client.PilotManagerClient import PilotManagerClient
+from DIRAC.WorkloadManagementSystem.JobWrapper.JobWrapper import RESCHEDULED
 from DIRAC.WorkloadManagementSystem.Utilities.Utils import createJobWrapper
 
 
@@ -712,9 +714,9 @@ def _checkSubmittedJobs(self):
                 self._rescheduleFailedJob(jobID, result["Message"])
                 self.hostFailureCount += 1
 
-            # The payload failed (if result["Value"] is not 0)
-            elif result["Value"]:
-                # In order to avoid overriding perfectly valid states, the status is updated iff the job was running
+            # The payload failed (if result["Value"] is not 0 and the job was not rescheduled)
+            elif result["Value"] and result["Value"] != RESCHEDULED:
+                # In order to avoid overriding perfectly valid states, the status is updated if the job was running
                 res = JobMonitoringClient().getJobsStatus(jobID)
                 if not res["OK"]:
                     return res
diff --git a/src/DIRAC/WorkloadManagementSystem/JobWrapper/JobWrapper.py b/src/DIRAC/WorkloadManagementSystem/JobWrapper/JobWrapper.py
index f203d2e4fbf..23ef2c38a7f 100755
--- a/src/DIRAC/WorkloadManagementSystem/JobWrapper/JobWrapper.py
+++ b/src/DIRAC/WorkloadManagementSystem/JobWrapper/JobWrapper.py
@@ -56,6 +56,14 @@
 
 CHILD_PID_POLL_INTERVALS = list(range(5, 40, 5))
 
+SUBMISSION_FAILED = -1
+SUBMISSION_REPORT_FAILED = -2
+JOBWRAPPER_EXCEPTION = -3
+INITIALIZATION_FAILED = 1
+PAYLOAD_FAILED = 2
+FINALIZATION_FAILED = 3
+RESCHEDULED = 4
+
 
 class JobWrapper:
     """The only user of the JobWrapper is the JobWrapperTemplate"""
diff --git a/src/DIRAC/WorkloadManagementSystem/JobWrapper/JobWrapperTemplate.py b/src/DIRAC/WorkloadManagementSystem/JobWrapper/JobWrapperTemplate.py
index 892e10e3946..eb7fcdc5837 100644
--- a/src/DIRAC/WorkloadManagementSystem/JobWrapper/JobWrapperTemplate.py
+++ b/src/DIRAC/WorkloadManagementSystem/JobWrapper/JobWrapperTemplate.py
@@ -1,16 +1,16 @@
 #!/usr/bin/env python
-""" This template will become the job wrapper that's actually executed.
+"""This template will become the job wrapper that's actually executed.
 
-    The JobWrapperTemplate is completed and invoked by the jobAgent and uses functionalities from JobWrapper module.
-    It has to be an executable.
+The JobWrapperTemplate is completed and invoked by the jobAgent and uses functionalities from JobWrapper module.
+It has to be an executable.
 
-    The JobWrapperTemplate will reschedule the job according to certain criteria:
-    - the working directory could not be created
-    - the jobWrapper initialization phase failed
-    - the inputSandbox download failed
-    - the resolution of the inpt data failed
-    - the JobWrapper ended with the status DErrno.EWMSRESC
+The JobWrapperTemplate will reschedule the job according to certain criteria:
+- the working directory could not be created
+- the jobWrapper initialization phase failed
+- the inputSandbox download failed
+- the resolution of the inpt data failed
 """
+
 import json
 import os
 import sys
@@ -24,6 +24,8 @@
 Script.parseCommandLine()
 
 from DIRAC import gLogger
+
+from DIRAC.WorkloadManagementSystem.JobWrapper import JobWrapper as JW
 from DIRAC.WorkloadManagementSystem.Client.JobReport import JobReport
 from DIRAC.WorkloadManagementSystem.JobWrapper.JobWrapperUtilities import (
     createAndEnterWorkingDirectory,
@@ -52,7 +54,7 @@ def execute(jobID: int, arguments: dict, jobReport: JobReport):
     if "InputSandbox" in arguments["Job"]:
         jobReport.commit()
         if not transferInputSandbox(job, arguments["Job"]["InputSandbox"]):
-            return 1
+            return JW.INITIALIZATION_FAILED
     else:
         gLogger.verbose("Job has no InputSandbox requirement")
 
@@ -61,7 +63,7 @@ def execute(jobID: int, arguments: dict, jobReport: JobReport):
     if "InputData" in arguments["Job"]:
         if arguments["Job"]["InputData"]:
             if not resolveInputData(job):
-                return 1
+                return JW.INITIALIZATION_FAILED
         else:
             gLogger.verbose("Job has a null InputData requirement:")
             gLogger.verbose(arguments)
@@ -71,7 +73,7 @@ def execute(jobID: int, arguments: dict, jobReport: JobReport):
     jobReport.commit()
 
     if not executePayload(job):
-        return 1
+        return JW.INITIALIZATION_FAILED
 
     if "OutputSandbox" in arguments["Job"] or "OutputData" in arguments["Job"]:
         if not processJobOutputs(job):
@@ -85,7 +87,7 @@ def execute(jobID: int, arguments: dict, jobReport: JobReport):
 ##########################################################
 
 
-ret = -3
+ret = JW.JOBWRAPPER_EXCEPTION
 try:
     jsonFileName = os.path.realpath(__file__) + ".json"
     with open(jsonFileName) as f:
@@ -105,9 +107,9 @@ def execute(jobID: int, arguments: dict, jobReport: JobReport):
     gLogger.exception("JobWrapperTemplate exception")
     try:
         jobReport.commit()
-        ret = -1
+        ret = JW.SUBMISSION_FAILED
     except Exception:  # pylint: disable=broad-except
         gLogger.exception("Could not commit the job report")
-        ret = -2
+        ret = JW.SUBMISSION_REPORT_FAILED
 
 sys.exit(ret)