In my case I got the desired functionality by replacing HashMap with:
http://docs.oracle.com/javase/7/docs/api/java/util/LinkedHashMap.html

"This implementation spares its clients from the unspecified, generally chaotic 
ordering provided by HashMap"

"This technique is particularly useful if a module takes a map on input, copies 
it, and later returns
 results whose order is determined by that of the copy. (Clients generally 
appreciate having things
 returned in the same order they were presented.)"

Anders

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