diff --git a/Code/Mantid/Framework/Kernel/test/MemoryTest.h b/Code/Mantid/Framework/Kernel/test/MemoryTest.h
index 80463928fde042fab84f34a3077dc0d91f4d6ac8..e6bc7aadec4647aea316d3ff3efe94435ab14e8e 100644
--- a/Code/Mantid/Framework/Kernel/test/MemoryTest.h
+++ b/Code/Mantid/Framework/Kernel/test/MemoryTest.h
@@ -33,11 +33,11 @@ public:
     TS_ASSERT_LESS_THAN_EQUALS(0, mem.availMem() );
     TS_ASSERT_DIFFERS( mem.availMemStr(), "" );
     TS_ASSERT_LESS_THAN_EQUALS(0, mem.reservedMem());
-    TS_ASSERT_LESS_THAN_EQUALS(0, mem.totalMem());
+    TS_ASSERT_LESS_THAN(0, mem.totalMem()); // The machine must have some memory
     TS_ASSERT_DIFFERS( mem.totalMemStr(), "" );
     
     // Current process stats
-    TS_ASSERT_LESS_THAN_EQUALS(0, mem.residentMem());
+    TS_ASSERT_LESS_THAN(0, mem.residentMem()); // Current process must use something
     TS_ASSERT_DIFFERS( mem.resUsageStr(), "");
     TS_ASSERT_LESS_THAN_EQUALS(0, mem.virtualMem());
     TS_ASSERT_DIFFERS( mem.vmUsageStr(), "");