diff --git a/Framework/Crystal/test/SortPeaksWorkspaceTest.h b/Framework/Crystal/test/SortPeaksWorkspaceTest.h
index 9bf9820de16e99cb0dca58a03fdf0fafa3c47864..d889eff22256dad0058cd005f259dbccb19d064c 100644
--- a/Framework/Crystal/test/SortPeaksWorkspaceTest.h
+++ b/Framework/Crystal/test/SortPeaksWorkspaceTest.h
@@ -8,6 +8,7 @@
 
 #include "MantidAPI/TableRow.h"
 #include "MantidCrystal/SortPeaksWorkspace.h"
+#include "MantidDataObjects/LeanElasticPeaksWorkspace.h"
 #include "MantidDataObjects/PeaksWorkspace.h"
 #include "MantidTestHelpers/WorkspaceCreationHelper.h"
 #include <algorithm>
@@ -209,4 +210,34 @@ public:
                       "workspaces should be the same.",
                       outWS, inWS);
   }
+
+  void test_leanPeakWorkspace_sort_inplace() {
+    // generate a lean elastic peak workspace with two peaks
+    auto lpws = std::make_shared<LeanElasticPeaksWorkspace>();
+    // add peaks
+    LeanElasticPeak pk1(Mantid::Kernel::V3D(0.0, 0.0, 6.28319), 2.0);
+    LeanElasticPeak pk2(Mantid::Kernel::V3D(6.28319, 0.0, 6.28319), 1.0);
+    lpws->addPeak(pk1);
+    lpws->addPeak(pk2);
+    IPeaksWorkspace_sptr inWS =
+        std::dynamic_pointer_cast<IPeaksWorkspace>(lpws);
+
+    SortPeaksWorkspace alg;
+    alg.setChild(true);
+    alg.setRethrows(true);
+    TS_ASSERT_THROWS_NOTHING(alg.initialize())
+    TS_ASSERT(alg.isInitialized())
+    TS_ASSERT_THROWS_NOTHING(alg.setProperty("InputWorkspace", inWS));
+    alg.setPropertyValue("OutputWorkspace", "OutName");
+    TS_ASSERT_THROWS_NOTHING(alg.setProperty("OutputWorkspace", inWS));
+    TS_ASSERT_THROWS_NOTHING(alg.setPropertyValue("ColumnNameToSortBy", "h"));
+    TS_ASSERT_THROWS_NOTHING(alg.execute());
+    TS_ASSERT(alg.isExecuted());
+
+    IPeaksWorkspace_sptr outWS = alg.getProperty("OutputWorkspace");
+
+    TSM_ASSERT_EQUALS("Sorting should have happened in place. Output and input "
+                      "workspaces should be the same.",
+                      outWS, inWS);
+  }
 };