diff --git a/lib/cmdlib.py b/lib/cmdlib.py
index e3fb2292bd57521cf5351621f41f0b1d58f0fb0b..f089b160b206a836aae5bcfa6d34ee1cdde3820f 100644
--- a/lib/cmdlib.py
+++ b/lib/cmdlib.py
@@ -9618,10 +9618,6 @@ class LUExportInstance(LogicalUnit):
     self.x509_key_name = self.op.x509_key_name
     self.dest_x509_ca_pem = self.op.destination_x509_ca
 
-    if self.op.remove_instance and not self.op.shutdown:
-      raise errors.OpPrereqError("Can not remove instance without shutting it"
-                                 " down before")
-
     if self.op.mode == constants.EXPORT_MODE_REMOTE:
       if not self.x509_key_name:
         raise errors.OpPrereqError("Missing X509 key name for encryption",
@@ -9687,6 +9683,11 @@ class LUExportInstance(LogicalUnit):
           "Cannot retrieve locked instance %s" % self.op.instance_name
     _CheckNodeOnline(self, self.instance.primary_node)
 
+    if (self.op.remove_instance and self.instance.admin_up and
+        not self.op.shutdown):
+      raise errors.OpPrereqError("Can not remove instance without shutting it"
+                                 " down before")
+
     if self.op.mode == constants.EXPORT_MODE_LOCAL:
       self.op.target_node = _ExpandNodeName(self.cfg, self.op.target_node)
       self.dst_node = self.cfg.GetNodeInfo(self.op.target_node)
diff --git a/qa/ganeti-qa.py b/qa/ganeti-qa.py
index 79a5d6e2be130d18f0054db60e54e350ca34f27c..afcdf18b9abeaeef1384247e096a71127e989785 100755
--- a/qa/ganeti-qa.py
+++ b/qa/ganeti-qa.py
@@ -430,15 +430,19 @@ def main():
 
     if (qa_config.TestEnabled('instance-add-plain-disk') and
         qa_config.TestEnabled("instance-export")):
-      instance = RunTest(qa_instance.TestInstanceAddWithPlainDisk, pnode)
-      expnode = qa_config.AcquireNode(exclude=pnode)
-      try:
-        RunTest(qa_instance.TestInstanceExportWithRemove, instance, expnode)
-        RunTest(qa_instance.TestBackupList, expnode)
-      finally:
-        qa_config.ReleaseNode(expnode)
-      del expnode
-      del instance
+      for shutdown in [False, True]:
+        instance = RunTest(qa_instance.TestInstanceAddWithPlainDisk, pnode)
+        expnode = qa_config.AcquireNode(exclude=pnode)
+        try:
+          if shutdown:
+            # Stop instance before exporting and removing it
+            RunTest(qa_instance.TestInstanceShutdown, instance)
+          RunTest(qa_instance.TestInstanceExportWithRemove, instance, expnode)
+          RunTest(qa_instance.TestBackupList, expnode)
+        finally:
+          qa_config.ReleaseNode(expnode)
+        del expnode
+        del instance
 
   finally:
     qa_config.ReleaseNode(pnode)